Program and Abstracts - Auburn...

Program and Abstracts

Sponsored by

Society for Industrial and Applied Mathematics (SIAM)College of Sciences and Mathematics, Auburn University

Department of Mathematics and Statistics, Auburn University

The 44th SIAM Southeastern Atlantic Section Conference

Auburn UniversityMarch 14–15, 2020

Organizing Committee

Yanzhao Cao (Conference Chair, SIAM SEAS President), Auburn University

Dmitry Glotov (Student Award Chair), Auburn University

Thi Thao Phuong Hoang, Auburn University

Junshan Lin (Conference Co-chair), Auburn University

Kelsey Ulmer (SIAM Auburn University Chapter President), Auburn University

Hans Werner Van Wyk, Auburn University

Guannan Zhang (Conference Co-chair), Oak Ridge National Lab

Contact

Address: Parker Hall 221, Department of Mathematics and Statistics, Auburn University

Tel: 334-844-6581

Email: [email protected]

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Table of contents

The 44th SIAM Southeastern Atlantic Section Conference Pro-gram

Table of contents

1 Venue Information, Map, and Conference Schedule . . . . . . . . . . . . . . . 7

2 Plenary Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 List of Mini-symposia and Contributed Talks . . . . . . . . . . . . . . . . . . . 19

4 Abstracts of Mini-symposia and Contributed Talks . . . . . . . . . . . . . . . 41

5

Venue Information, Map, and Conference Schedule

1 Venue Information, Map, and Conference Schedule

7


Venue Information

• The conference will take place at the Mell Classroom Building located at 231 Mell Street.

• Free parking is available during the conference at the Library Parking Deck (5 RooseveltDr), which is adjacent to Mell Classroom Building.

• The reception and the poster session will be held in the Auburn University Hotel andConference Center.

8


Mell Classroom Building Floor Plan

Second floor

9


Third floor

Fourth floor

10


Conference Schedule

Saturday, March 14

7:30AM-8:20AM Registration Lobby at MellClassroom

8:20AM-8:30AM Welcome Remarks Mell 2510

8:30AM-9:30AM Plenary Talk I: Jianfeng Lu Mell 2510

9:30AM-10:00AM Coffee Break Lobby at MellClassroom

10:00AM-12:00PMParallel Session 1

MS1:Advances in Numerical Methods for Multi-physicsProblems - Part I Libry 3129

MS2:Recent Developments in Numerical Algorithmsfor PDEs - Part I Libry 3127

MS3: Recent Developments of Numerical Methods forFluid Flows and Applications - Part I Libry 3027

MS4: Recent Developments in Nonlocal ContinuumModeling - Part I Libry 4129

MS5: Modeling, Analysis, Approximation andParameter Identification of Fractional PDEs andNonlocal Models - Part I

Libry 4127

MS6: Recent Developments and Applications inComputational Biology - Part I Libry 4027

MS7: Classic and Deep Learning Methods for DataDriven Models - Part I Libry 3033

MS8: Theory and Practice of Machine Learning - PartI Libry 3035

MS9: Advances in Theory and Methods forHigh-dimensional Approximations - Part I Libry 3041

MS10: Advances in Mathematical Finance andOptimization - Part I Mell 3520

MS11: Reduced Order Models and Data - Part I Libry 4035

MS12: Theory and Numerics for Resonances andRelated Eigenvalue Problems in Optics andElectromagnetics - Part I

Libry 4041

MS16: Novel Techniques in Optimization andApplications Libry 4033

CS: Contributed Session - Part I Mell 4520

12:00PM-2:00PM Lunch Break

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Saturday, March 14

2:00PM-3:00PM Plenary Talk II: Oscar Bruno Mell 2510

3:00PM-3:30PM Coffee Break Lobby at MellClassroom

3:30PM-5:30PMParallel Session 2

MS1:Advances in Numerical Methods for Multi-physicsProblems - Part II Libry 3129

MS2:Recent Developments in Numerical Algorithmsfor PDEs - Part II Libry 3127

MS3: Recent Developments of Numerical Methods forFluid Flows and Applications - Part II Libry 3027

MS4: Recent Developments in Nonlocal ContinuumModeling - Part II Libry 4129

MS5: Modeling, Analysis, Approximation andParameter Identification of Fractional PDEs andNonlocal Models - Part II

Libry 4127

MS6: Recent Developments and Applications inComputational Biology - Part II Libry 4027

MS7: Classic and Deep Learning Methods for DataDriven Models - Part II Libry 3033

MS8: Theory and Practice of Machine Learning - PartII Libry 3035

MS9: Advances in Theory and Methods forHigh-dimensional Approximations - Part II Libry 3041

MS10: Advances in Mathematical Finance andOptimization - Part II Mell 3520

MS12: Theory and Numerics for Resonances andRelated Eigenvalue Problems in Optics andElectromagnetics - Part II

Libry 4041

MS13: Recent Development of Coupled Problems withAdvanced Physics Based Numerical Methods- Part I Libry 4035

MS20: Dynamics of Partial Differential Equations Libry 4033

CS: Contributed Session - Part II Mell 4520

6:00PM-8:00PM Reception (Dinner) at AU Hotel and Conference Center

12


Sunday, March 15

8:30AM-9:30AM Plenary Talk III: James Nagy Mell 2510

9:30AM-9:40AM Student Award Ceremony Mell 2510

9:40AM-10:00AM Coffee Break Lobby at MellClassroom

10:00AM-12:00PMParallel Session 3

MS1:Advances in Numerical Methods for Multi-physicsProblems - Part III Libry 3129

MS2:Recent Developments in Numerical Algorithmsfor PDEs - Part III Libry 3127

MS4: Recent Developments in Nonlocal ContinuumModeling - Part III Libry 4129

MS10: Advances in Mathematical Finance andOptimization - Part III Mell 3520

MS11: Reduced Order Models and Data - Part II Libry 4041

MS13:Recent Development of Coupled Problems withAdvanced Physics Based Numerical Methods - Part II Libry 4035

MS14: Some Numerical Algorithms in ScientificMachine Learning Libry 3027

MS15: Stochastic Optimal Control and ItsApplications Libry Libry 3033

MS17: Theory and Computation for Stochastic ModelsLibry Libry 3035

MS18: Recent Development of Finite ElementMethods and Related Applications Libry 4127

MS19: Young Researchers in Mathematical Biology Libry 4027

CS: Contributed Session - Part III Mell 4520

13

Plenary Talks

2 Plenary Talks

15

Plenary Talks

Solving Eigenvalue Problems in High Dimension

Speaker: Jianfeng Lu, Department of Mathematics, Duke University

Scheduled: Saturday, March 14 8:30AM–9:30AM at Mell Classroom 2510

Details: Plenary Talk I

Abstract: The leading eigenvalue problem of a differential operator arises in many scientific andengineering applications, such as quantum many-body problems. Conventional algo-rithms become impractical due to the huge computational and memory complexityfrom the curse of dimensionality. In this talk, we will discuss some recent workson new algorithms for eigenvalue problems in high dimension based on randomizedand coordinate-wise methods and also machine learning approaches. (joint work withJiequn Han, Yingzhou Li, Zhe Wang and Mo Zhou).

Simulation, Optimization and Design Methods for Electromagnetic Metama-terial Devices

Speaker: Oscar Bruno, Department of Computing and Mathematical Sciences, Caltech

Scheduled: Saturday, March 14 2:00PM–3:00PM at Mell Classroom 2510

Details: Plenary Talk II

Abstract: We present fast spectral electromagnetic solvers that address some of the main difficul-ties associated with the simulation of realistic engineering electromagnetic problems inthe frequency- and time-domain. Based on use of Green functions and fast high-ordermethods for evaluation of integral operators, these algorithms can solve, with high-order accuracy, problems of electromagnetic propagation and scattering for large andcomplex three-dimensional structures and devices – such as silicon devices, structuredlenses, and metamaterials. In particular, we will consider the important but challengingproblem of design and optimization of optical and photonic devices of large electricalsize. A variety of applications will be presented demonstrating the significant designcapabilities inherent in the new methods, as well as the improvements these algorithmscan provide, over other approaches, in generality, accuracy, and speed.

16

Plenary Talks

MATLAB Tools for Large-Scale Linear Inverse Problems

Speaker: James Nagy, Department of Mathematics, Emory University

Scheduled: Sunday, March 15 8:30AM–9:30AM at Mell Classroom 2510

Details: Plenary Talk III

Abstract: Inverse problems arise in a variety of applications: image processing, finance, math-ematical biology, and more. Mathematical models for these applications may involveintegral equations, partial differential equations, and dynamical systems, and solutionschemes are formulated by applying algorithms that incorporate regularization tech-niques and/or statistical approaches. In most cases these solutions schemes involvethe need to solve a large-scale ill-conditioned linear system that is corrupted by noiseand other errors. In this talk we describe and demonstrate capabilities of a new MAT-LAB software package that consists of state-of-the-art iterative methods for solvingsuch systems, which includes approaches that can automatically estimate regulariza-tion parameters, stopping iterations, etc., making them very simple to use. Thus,the package allows users to easily incorporate into their own applications (or simplyexperiment with) different iterative methods and regularization strategies with verylittle programming effort. On the other hand, sophisticated users can also easily accessvarious options to tune the algorithms for certain applications. Moreover, the packageincludes several test problems and examples to illustrate how the iterative methodscan be used on a variety of large-scale inverse problems.The talk will begin with a brief introduction to inverse problems, discuss considerationsthat are needed to compute an approximate solution, and describe some details aboutnew efficient hybrid Krylov subspace methods that are implemented in our package.These methods can guide users in automatically choosing regularization parameters,and can be used to enforce various regularization schemes, such as sparsity. We will useimaging examples that arise in medicine and astronomy to illustrate the performanceof the methods.This is joint work with Silvia Gazzola (University of Bath) and Per Christian Hansen(Technical University of Denmark).

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List of Mini-symposia and Contributed Talks

3 List of Mini-symposia and Contributed Talks

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MS1: Advances in numerical methods for multi-physics problems (Part I)

Organizers: Sibusiso Mabuza, Clemson UniversityHyesuk Lee, Clemson UniversitySidafa Conde, Sandia National Laboratories

Talks & Speakers:

Scheduled at:

Parallel Session 1

Saturday, March14, 10:00–12:00

Room: Libry 3129

1. A hybridizable discontinuous method for flow and transportphenomena in porous mediaMaurice S. Fabien, Brown University

2. Patient-specific modeling of coronary bioresorbable stentsAlessandro Veneziani, Emory University

3. Second order time discretization for a coupled quasi-Newtonian fluid-poroelastic systemHemanta Kunwar, Clemson University

4. Developing efficient IMEX Runge-Kutta methods for non-hydrostatic atmosphere modelsAndrew Steyer, Sandia National Laboratories

MS1: Advances in numerical methods for multi-physics problems (Part II)


Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 3129

1. High Rayleigh number variational multiscale large eddysimulations of Rayleigh-Benard convectionDavid Sondak, Harvard University

2. On Some complex coupled multi-physics PDE: combiningelectromagnetics and continuum mechanicsAmnon J Meir, Southern Methodist University

3. Adjoint based a posteriori error analysis for stationary re-sistive MHDAri Rappaport, University of New Mexico

4. Highly-scalable Poisson solvers on GPUsPedro Bello-Maldonado, UIUC

20


MS1: Advances in numerical methods for multi-physics problems (Part III)


Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Libry 3129

1. Discretization of the multi-fluid plasma model using IMEXand mixed continuous/discontinuous FEMSean Miller, Sandia National Laboratories

2. A five-moment multifluid model for partially Ionized plas-mas with arbitrarily many speciesMichael Crockatt, Sandia National Laboratories

3. Invariant domain preserving methods and convex limitingIgnancio Tomas, Sandia National Laboratories

4. On IMEX-AFC continuous finite element methods forvisco-resistive MHDSibusiso Mabuza, Clemson University

MS2: Recent Developments in Numerical Algorithms for PDEs (Part I)

Organizers: S. S. Ravindran, University of Alabama in Huntsville

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 3127

1. High-order multirate time integration for multiphysics PDEsystemsDan Reynolds, Southern Methodist University

2. On the shock-capturing discontinuous galerkin methodbased on the entropy principleYu Lv, Missisippi State University

3. Predictor/Corrector adaptive mesh refinement for somenonlinear finite element problemsTimo Heister, Clemson University

4. Variable stepsize, variable order methods for PDEsVictor DeCaria, Oak Ridge National Laboratory

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MS2: Recent Developments in Numerical Algorithms for PDEs (Part II)


Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 3127

1. New finite difference methods on irregular grids for solvingthe Maxwell’s equationsYingjie Liu, Georgia Tech

2. A supermesh method for computing solutions to the StefanproblemYang Liu, Florida State University

3. A C0 interior penalty method for the phase field crystalequationAmanda Diegel, Mississippi State University

4. Supersonic Euler and magnetohydrodynamic flow pastconesIan Holloway, Wright State University

MS2: Recent Developments in Numerical Algorithms for PDEs (Part III)


Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Libry 3127

1. DG methods for nonlinear wave equationsThomas Hagstrom, Southern Methodist University

2. Robust training and initialization of deep neural networks:an adaptive basis viewpointMamikon Gulian, Sandia National Labs

3. Discontinuous Galerkin methods for an elliptic state-constrained optimal control problemYi Zhang, University of North Carolina at Greensboro

4. Scalable computation of matrix functions for nonlinearPDEs through asymptotic analysis of block Krylov projec-tionJames Lambers, University of Southern Mississippi

22


MS3: Recent Developments of Numerical methods for Fluid Flows and Ap-plications (Part I)

Organizers: Thi-Thao-Phuong Hoang, Auburn University

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 3027

1. Weighted least-squares finite element methods for vis-coelastic fluid flowsHyesuk Lee, Clemson University

2. Accelerating solvers for degenerate problemsSara Pollock, University of Florida

3. Efficient ensemble algorithms for numerical approximationof stochastic Stokes-Darcy equationsNan Jiang, Missouri University of Science and Technology

4. A posteriori error estimates for weak Galerkin methods forStokes equations on polygonal meshesLin Mu, University of Georgia

MS3: Recent Developments of Numerical methods for Fluid Flows and Ap-plications (Part II)

Organizers: Thi-Thao-Phuong Hoang, Auburn University

Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 3027

1. Maximum bound principles for a class of semilinearparabolic equations and exponential time differencingSchemesLili Ju, University of South Carolina

2. Exponential integrators for meteorological equationsVu Thai Luan, Mississippi State University

3. Geometric multigrid for massively parallel, adaptive, largescale Stokes flowTimo Heister, Clemson University

4. Space-time domain decomposition methods for Stokes-Darcy couplingThi-Thao-Phuong Hoang, Auburn University

23


MS4: Recent Developments in Nonlocal Continuum Modeling (Part I)

Organizers: James Scott, University of TennesseePablo Seleson, Oak Ridge National Laboratory

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 4129

1. Nonlocal brittle fracture modeling with applied tractionforcesRobert Lipton, Louisiana State University

3. Overall equilibrium in the coupling of peridynamics andclassical continuum mechanicsPablo Seleson, Oak Ridge National Laboratory

3. Regularity of solutions to nonlinear nonlocal equations andsystems in continuum mechanicsJames Scott, University of Tennessee

4. New families of fractional PDEs arising from fractional cal-culus of variationsMitchell Sutton, University of Tennessee

MS4: Recent Developments in Nonlocal Continuum Modeling (Part II)


Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 4129

1. Fractional order viscoelastic modeling and Bayesian uncer-tainty analysis of elastomers and auxetic foamsWilliam Oates, Florida State University

2. Fractional optimal control problems with state constraints:algorithm and analysisDeepanshu Verma, George Mason University

3. A convergent monotone scheme for a nonlocal segregationmodel with free boundaryXiaochuan Tian, University of Texas at Austin

4. The Evolution of scientific collaborations in peridynamicsBiraj Dahal, Clemson University

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MS4: Recent Developments in Nonlocal Continuum Modeling (Part III)


Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–11:30

Room: Libry 4129

1. A fast numerical method for a state-based PD modelHong Wang, University of South Carolina

2. Convergence studies in meshfree peridynamic wave andcrack propagationMarco Pasetto, University of California, San Diego

3. An RBF quadrature rule approach for solving nonlocal con-tinuum modelsIsaac Lyngaas, Oak Ridge National Laboratory

4. Implementation of a parallel MHD FEM FMM solverK. Daniel Brauss, Francis Marion University

MS5: Modeling, Analysis, Approximation and Parameter Identification ofFractional PDEs and Nonlocal Models (Part I)

Organizers: Hong Wang, University of South CarolinaYong Zhang, University of AlabamaXiangcheng Zheng, University of South CarolinaBingqing Lu, University of Alabama

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 4127

1. Lagrangian approximation of vector fractional diffusionwith reactions in bounded domainsYong Zhang, University of Alabama

2. Mathematical modeling of variable-order fractional differ-ential equationsHong Wang, University of South Carolina

3. Self-Singularity capturing and fast IMEX schemes for non-linear stochastic fractional differential equationsJorge Suzuki, Michigan State University

4. Fast Petrov-Galerkin spectral methods for fixed-to-distributed FPDEs in high dimensionsMehdi Samiee, Michigan State University

25


MS5: Modeling, Analysis, Approximation and Parameter Identification ofFractional PDEs and Nonlocal Models (Part II)

Organizers: Hong Wang, University of South CarolinaYong Zhang, University of AlabamaXiangcheng Zheng, University of South CarolinaBingqing Lu, University of Alabama

Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 4127

1. New characterizations of Sobolev and potential spacesJames Scott & Tadele Mengesha, University of Tennessee

2. Fractional advection-dispersion-reaction equation (f-ADRE) to capture nitrate fate and transport in soilBingqing Lu & Yong Zhang, University of Alabama

3. Analysis and numerical approximations of variable-ordertime and space-time fractional diffusion equationsXiangcheng Zheng, University of South Carolina

4. Analysis and numerical inversion of the inverse problem ofdetermining the variable fractional order in variable-ordertime-fractional diffusion equationsYiqun Li, University of South Carolina

MS6: Recent Developments and Applications in Computational Biology(Part I)

Organizers: Shan Zhao, University of AlabamaXinfeng Liu, University of South Carolina

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 4027

1. A Newton-like iterative method for solving the Poisson-Boltzmann equation and its implementation in the DelPhisuiteChuan Li, West Chester University

2. Micro-macro coupling of fluid dynamics in complex fluidPaula Vasquez, University of South Carolina

3. Mathematical modeling reveals a noncanonical feedback be-tween messenger RNA and microRNATian Hong, University of Tennessee

4. Boundary conditions and numerical techniques for catch-ing the Gaussian curvature in hybrid modeling of protein-membrane interactionsYongcheng Zhou, Colorado State University

26


MS6: Recent Developments and Applications in Computational Biology(Part II)

Organizers: Shan Zhao, University of AlabamaXinfeng Liu, University of South Carolina

Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 4027

1. A Hybrid model for simulating sprouting angiogenesis inbiofabricationYi Sun, University of South Carolina

2. French ducks in the heart: canard analysis can explainvoltage-driven early afterdepolarization phenomena in car-diac CellsJoshua Kimrey, Florida State University

3. Mathematical modeling, computation and experimental in-vestigation of dynamical heterogeneity in breast cancerXinfeng Liu, University of South Carolina

4. A regularization approach for biomolecular electrostaticsinvolving singular charge sources and diffuse interfacesShan Zhao, University of Alabama

MS7: Classic and Deep Learning Methods for Data Driven Models (Part I)

Organizers: Zhu Wang, University of South CarolinaLili Ju, University of South Carolina

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 3033

1. Information Newton’s flow: second-order optimizationmethod in probability spaceWuchen Li, University of California, Los Angeles

2. Nonlinear level-sets learning for dimensionality reductionin high-dimensional function approximationGuannan Zhang, Oak Ridge National Laboratory

3. Closure learning for nonlinear model reduction using deepresidual neural networkXuping Xie, Courant Institue, NYU

27


MS7: Classic and Deep Learning Methods for Data Driven Models (Part II)

Organizers: Zhu Wang, University of South CarolinaLili Ju, University of South Carolina

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 3033

1. Scale-equivariant CNN with decomposed convolutional fil-tersWei Zhu, Duke University

2. Machine learning for missing dynamicsHaizhao Yang, Purdue University

3. Data-driven approaches for parameterized diffusion prob-lemsYuankai Teng, University of South Carolina

MS8: Theory and Practice of Machine Learning (Part I)

Organizers: Viktor Reshniak, Oak Ridge National LaboratoryJoseph Daws, University of Tennessee Knoxville

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 3035

1. A neural network for solving the Poisson equation with ho-mogeneous boundary conditionsJoseph Daws, University of Tennessee Knoxville

2. Train like a (Var)Pro: efficient training of neural networkswith variable projectionElizabeth Newmani, Emory University

3. NLP technique associated learning model for predictive an-alyticsDon Hong, Middle Tennessee State University

4. Machine learning for classification and segmentation of lungnodules in CT-scansJerry F. Magnan, Florida State University

28


MS8: Theory and Practice of Machine Learning (Part II)

Organizers: Viktor Reshniak, Oak Ridge National LaboratoryJoseph Daws, University of Tennessee Knoxville

Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 3035

1. Robust learning with implicit residual networksViktor Reshniak, Oak Ridge National Laboratory

2. Bayesian topological learningCassie Putman Micucci, University of Tennessee Knoxville

3. Active learning of tissue-mimicking 3D-printing under cen-soring, with application for surgical planningJialei Chen, Georgia Institute of Technology

4. High-fidelity computed tomography: from model-based todata-driven approachesSinganallur Venkatakrishnan, Oak Ridge National Laboratory

MS9: Advances in Theory and Methods for High-dimensional Approxima-tions (Part I)

Organizers: Hoang Tran, Oak Ridge National LaboratoryArmenak Petrosyan, Oak Ridge National Laboratory

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 3041

1. Neural network integral representations and sparse net-worksArmenak Petrosyan, Oak Ridge National Laboratory

2. Identification of linear dynamical systems via dataFatih Gelir, University of Texas at Dallas

3. Effects of depth, width and initialization: a convergenceanalysis of layer-wise training for deep linear networksYeonjong Shin, Brown University

4. Asymptotic properties of the minimizers of short rangescale-invariant interaction energiesAlex Vlasiuk, Florida State University

29


MS9: Advances in Theory and Methods for High-dimensional Approxima-tions (Part II)

Organizers: Hoang Tran, Oak Ridge National LaboratoryArmenak Petrosyan, Oak Ridge National Laboratory

Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 3041

1. Data-driven tensor decompositionTingran Gao, University of Chicago

2. Estimates of entropy numbers in high-dimensional spaceand applications to compressed sensingHoang Tran, Oak Ridge National Laboratory

3. Tensor completion through total variation with initializa-tion from weighted HOSVDLongxiu Huang, University of California, Los Angeles

MS10: Advances in Mathematical Finance and Optimization (Part I)

Organizers: Ekren Ibrahim, Florida State UniversityArash Fahim, Florida State University

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Mell 3520

1. Systemic risk in networks with a central nodeHamed Amini, Georgia State University

2. Multilevel Monte Carlo for LIBOR market modelArun Kumar Polala, Florida State University

3. Monitoring in principal-agent problemArash Fahim, Florida State University

4. Sharing profits in the sharing economyGu Wang, Worcester Polytechnic Institute

30


MS10: Advances in Mathematical Finance and Optimization (Part II)


Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Mell 3520

1. Coupling and characterization of solutions to BSDEsGordan Zitkovic, University of Texas at Austin

2. A polynomial chaos-based approach to brownian path gen-erationJamie Fox, Florida State University

3. Path-dependent PDEs and optimal control in infinite di-mensionsChristian Keller, University of Central Florida

4. A general solution technique for insider problems using op-timal transportFrancois Cocquemas, Florida State University

MS10: Advances in Mathematical Finance and Optimization (Part III)


Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Mell 3520

1. Asymptotics for the time-discretized log-normal SABRmodelDan Pirjol, Stevens Institute of Technology

2. Quasi-Monte Carlo simulation of copulas for option pricingand VaR estimationYiran Chen, Florida State University

3. Delivering multi-specialty care via online telemedicine plat-formsLingjiong Zhu, Florida State University

4. Constrained non-concave utility maximization of a variableannuity policyholderAdriana Ocejo Monge, University of North Carolina at Charlotte

31


MS11: Reduced Order Models and Data (Part I)

Organizers: Jeff Borggaard, Virginia TechHonghu Liu, Virginia Tech

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 4035

1. The polynomial-quadratic regulator control problemJeff Borggaard, Virginia Tech

2. Data-driven variational multiscale reduced order modelsBirgul Koc, Virginia Tech

3. Reduced order models for variable density flow and trans-port equationsOlcay Cifti, Auburn University

4. Data-driven closure strategies for reduced order models ofthe quasi geostrophicChanghong Mou, Virginia Tech

MS11: Reduced Order Models and Data (Part II)

Organizers: Jeff Borggaard, Virginia TechHonghu Liu, Virginia Tech

Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–11:30

Room: Libry 4041

1. Quasi-optimal sparse grids method for periodic functionsMiroslav Stoyanov, Oak Ridge National Laboratory

2. Efficient sampling methods for uncertainty quantificationover variable resolution parameter spacesHans-Werner van Wyk, Auburn University

3. A sparse-grid probabilistic scheme for approximation of therunway probability of electrons in fusion tokamak simula-tionMinglei Yang, Oak Ridge National Laboratory

32


MS12: Theory and Numerics for Resonances and Related Spectral Problemsin Optics and Electromagnetics (Part I)

Organizers: Junshan Lin, Auburn University

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 4041

1. Aspects of the spectrum of multi-layer graphene-type graphoperatorsStephen P Shipman, Louisiana State University

2. Finite element approximation of nonlinear eigenvalue prob-lemsJiguang Sun, Michigan Technological University

3. Controlling refraction using sub-wavelength resonatorsYue Chen, Auburn University at Montgomery

4. Electron dynamics in novel materials: waves at degenera-cies and edgesAlexander Watson, Duke University

MS12: Theory and Numerics for Resonances and Related Spectral Problemsin Optics and Electromagnetics (Part II)

Organizers: Junshan Lin, Auburn University

Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 4041

1. Convergence of an HDG finite element method forMaxwell’s equations in an inhomogeneous mediumPeter Monk, University of Delaware

2. Backward waves in corrugated wave guides with dispersioncontrolled by plasmonic resonancesRobert Lipton, Louisiana State University

3. A high-Order perturbation of envelopes (HOPE) methodfor scattering by periodic inhomogeneous mediaDavid Nicholls, University of Illinois at Chicago

4. Optical phenomena and resonances in the homogenizationof layered heterostructuresMatthias Maier, Texas A&M University

33


MS13: Recent Development of Coupled Problems with Advanced PhysicsBased Numerical Methods (Part I)

Organizers: Sanghyun Lee, Florida State University

Talks & Speakers:

Scheduled at:

Parallel Session 1


Room: Libry 4035

1. Enriched Galerkin for coupled flow and transportSanghyun Lee, Florida State University

2. Weak Galerkin finite element methods for Brinkman equa-tionsLin Mu, University of Georgia

3. Adaptive mesh refinement for Cut Finite Element MethodCuiyu He, University of Georgia

4. Simulation of precipitation reactions in microfluidic devicesPatrick Eastham, Florida State University

MS13: Recent Development of Coupled Problems with Advanced PhysicsBased Numerical Methods (Part II)

Organizers: Sanghyun Lee, Florida State University

Talks & Speakers:

Scheduled at:

Parallel Session 2

Sunday, March15, 10:00–12:00

Room: Libry 4035

1. High order FFT Poisson solvers for interface and boundaryvalue problemsShan Zhao, University of Alabama

2. Multirate exponential methods for additively partitionedsystems of differential equationsVu Thai Luan, Mississippi State University

3. Modelling the Navier-Stokes-Darcy-Heat systemMatt McCurdy, Florida State University

4. New central and central DG-type methods on overlappingcells for solving MHD equations on triangular meshesYingjie Liu, Georgia Tech

34


MS14: Some Numerical Algorithms in Scientific Machine Learning

Organizers: Hongchao Zhang, Louisiana State UniversityXiaoliang Wan, Louisiana State University

Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Libry 3027

1. Deep density estimation via invertible block-triangularmappingXiaoliang Wan, Louisiana State University

2. A self-consistent-field iteration for orthogonal canonicalcorrelation analysisLi Wang, University of Texas at Arlington

3. Extending the added-mass partitioned (AMP) scheme forsolving FSI problems coupling incompressible flows withelastic beams to 3DLongfei Li, University of Louisiana at Lafayette

4. A derivative-free geometric algorithm for optimization ona sphereHongchao Zhang, Louisiana State University

MS15: Stochastic Optimal Control and Its Applications

Organizers: Feng Bao, Florida State UniversityJiongmin Yong, University of Central Florida

Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Libry 3033

1. Linear-quadratic optimal control with random coefficientsJiongmin Yong, University of Central Florida

2. On the asymptotic optimality of the comb strategy for pre-diction with expert adviceIbrahim Ekren, Florida State University

3. A global Maximum principle for stochastic optimal controlproblems with delayJingtao Shi, Shandong University

4. Stochastic optimal impulse control with decision lagsChang Li, University of Central Florida

35


MS16: Novel Techniques in Optimization and Applications

Organizers: Guohui Song, Old Dominion University

Talks & Speakers:

Scheduled at:

Parallel Session 1

Saturday March14, 10:00–11:30

Room: Libry 4033

1. Optimization in infinite-dimensional spacesGuohui Song, Old Dominion University

2. Logic-based benders decomposition for gantry cranescheduling with transferring position constraints in a rail-road container terminalYi Wang, Auburn University at Montgomery

3. Polynomial filters of graph shifts and their inverses: theoryand local implementationNazar Emirov, University of Central Florida

MS17: Theory and Computation for Stochastic Models

Organizers: Xu Wang, Purdue UniversityFeng Bao, Florida State University

Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Libry 3035

1. Structure-preserving numerical method for stochastic non-linear Schrodinger equationJianbo Cui, Georgia Tech

2. Analytic continuation of noisy data using Adams BashforthResNetXuping Xie, Courant Institute, NYU

3. A splitting up scheme for backward doubly stochastic dif-ferential equationsHe Zhang, Auburn University

4. Inverse random source scattering for the Helmholtz equa-tion with attenuationXu Wang, Purdue University

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MS18: Recent Development of Finite Element Methods and Related Appli-cations

Organizers: Cuiyu He, University of GeorgiaLin Mu, University of Georgia

Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Libry 4127

1. Cut finite element method for ill-posed Bernoulli freeboundary problemCuiyu He, University of Georgia

2. Adaptive weak Galerkin method for convection-diffusionproblemNatasha Sharma, University of Texas at El Paso

3. A stabilizer free weak Galerkin finite element method forgeneral second-order elliptic problemAhmed Al-Taweel, University of Arkansas at Little Rock

4. Pricing S&P 500 index option with Lévy JumpsBin Xie, University of Georgia

MS19: Young Researchers in Mathematical Biology

Organizers: Christopher Botelho, University of Central FloridaPoroshat Yazdanbakhshghahyazi, University of Central Florida

Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Room: Libry 4027

1. A tale of two microbes: an analysis of vibrio-phage inter-actionChristopher Botelho, University of Central Florida

2. Applications of target reproduction numbers in infectiousdisease modelsPoroshat Yazdanbakhshghahyazi, University of Central Florida

3. Modeling Disease Immunity Dynamics: Application toCholera ModelsHenry Chang, University of Miami

4. Analysis of mosquito population modelsHanna Reed

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MS20: Dynamics of Partial Differential Equations

Organizers: Xiaoying Han, Auburn University

Talks & Speakers:

Scheduled at:

Parallel Session 2


Room: Libry 4033

1. Global dynamics on 1D compressible MHDRonghua Pan, Georgia Tech

2. The dynamical behavior of solutions of nonlocal partial dif-ferential equationsXingjie Yan, China University of Mining and Technology

3. Turning point principle for the stability of stellar modelsZhiwu Lin, Georgia Tech

4. Time periodic solutions to the full hydrodynamic model tosemiconductorsMing Cheng, Jilin University

CS: Contributed Session (Part I)

Organizer: Sirani M. Perera, Embry-Riddle Aeronautical University

Talks & Speakers:

Scheduled at:

Parallel Session 1


Mell 4520

1. A fast delay Vandermonde solver for beamformingSirani M. Perera, Embry-Riddle Aeronautical University

2. A fast hybrid transform algorithm for beam digitizationLevi Lingsch, Embry-Riddle Aeronautical University

3. Resonant tori, transport barriers, and chaos in a vector fieldwith a Neimark-Sacker bifurcationEmmanuel Fleurantin, Florida Atlantic University

4. Clustering in sparse popularity adjusted stochastic blockmodeMajid Noroozi, University of Central Florida

5. Multiple linear regression: out-of-sample predictions withan example in healthcare stocksPhong Luu, University of North Georgia

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CS: Contributed Session (Part II)


Talks & Speakers:

Scheduled at:

Parallel Session 2


Mell 4520

1. Wide neural networks with bottlenecks are deep GaussianprocessesDevanshu Agrawal, University of Tennessee Knoxville

2. Adversarial machine learning: error and sensitivity charac-terizationAlison Jenkins, Auburn University

3. Existence of a solution for a generalized Forchheimer flowin porous mediaThinh Kieu, University of North Georgia

4. Optimizing numerical simulations of colliding galaxies I:theoretical and mathematical aspectsGraham West, Middle Tennessee State University

5. Optimizing numerical simulations of colliding galaxies II:fitting simulations to astronomical dataMatthew Ogden, Middle Tennessee State University

CS: Contributed Session (Part III)


Talks & Speakers:

Scheduled at:

Parallel Session 3

Sunday, March15, 10:00–12:00

Mell 4520

1. A Formulation of the porous medium equation with time-dependent porosity: a priori estimatesKoffi Fadimba, University of South Carolina Aiken

2. An efficient numerical method for modeling electromag-netic wave scattering by random surfacesKelsey Ulmer, Auburn University

3. Stochastic gradient descent and adaptive gradient descentalgorithms in control of stochastic partial differential equa-tionsSomak Das, Auburn University

4. Convective stability of carbon sequestration in porousmediumMahmoud DarAssi, Princess Sumaya University for Technology

5. Conservation laws in heterogenous mediaBaris Kopruluoglu, Auburn University

6. Quantitative analysis of scattering resonances for a 3D sub-wavelength cavityMaryam Fatima, Auburn University

39

Abstracts of Mini-symposia and Contributed Talks

4 Abstracts of Mini-symposia and Contributed Talks

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MS1: Advances in numerical methods for multi-physics problems (Part I)

Organizers: Sibusiso Mabuza, Clemson University

Hyesuk Lee, Clemson University

Sidafa Conde, Sandia National Laboratories

Description: The numerical modeling of multiphysics phenomena continues to be a subject of vi-brant research in computational science. Great progress is being made in differentfronts that enables us to simulate complex model equations for such challenging prob-lems. Numerical advances are on algorithms which include discretization techniquesand time integrators. Computational advances are on shared and distributed memoryparallel implementation, algebraic preconditioning strategies and various improvementsassociated with next generation computer architecture. This session will broadly lookat the numerical methods for highly coupled multiphysics problems in incompress-ible fluid flow, gas dynamics, fluid-structure interaction, magnetohydrodynamics andplasma physics. Topics such as the discretization of multiphysics equations using finiteelement and finite volume methods will be presented. The nonlinear and linear solvertechniques, strong stability preserving time stepping will be considered. Furthermore,stabilization techniques, statistical analysis among other topics will be presented.

Talksdetails:

1. A hybridizable discontinuous method for flow and transport phenomenain porous mediaMaurice S. Fabien, Brown University

2. Patient-specific modeling of coronary bioresorbable stentsAlessandro Veneziani, Emory University

Abstract. The interplay between geometry and hemodynamics is well known to be asignificant factor in the development of cardiovascular diseases. This is particularly truefor coronary arteries interested by a stenting procedure. To elucidate and quantify thisfactor, an accurate patient-specific analysis requires the reconstruction of the geometryleft by the prosthesis deployment for a computational fluid dynamics (CFD) investiga-tion. However, the accurate inclusion of the stent footprint in the domain used for thenumerical simulation is critical for detecting abnormal stress conditions and flow distur-bances, particularly for stents with thick struts like the bioresorbable ones. We presenta novel methodology of geometrical reconstruction, that relies on advanced concepts ofimage registration and computational geometry. Volumetric reconstruction of the stentfree of inconsistencies (self-intersections) that would undermine the meshing of the stentedartery is specifically addressed. We test our “data-assimilation” methodology based on acombination of OCT and angiographic image in the CFD analysis of several cases, bothspecifically designed (phantom) and clinically retrieved, demonstrating the accuracy andthe efficiency of our procedure. We also introduce the multiphysics problem of modelingof the strut absorption in view of the rigorous optimization of the stent design.

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3. Second order time discretization for a coupled quasi-Newtonian fluid-poroelastic systemHemanta Kunwar, Clemson University

Abstract. Numerical methods are proposed for the nonlinear Stokes-Biot system mod-eling interaction of a free fluid with a poroelastic structure. We discuss time discretiza-tion and decoupling schemes that allow the fluid and the poroelastic structure computedindependently using a common stress force along the interface. The coupled system ofnonlinear Stokes and Biot is formulated as a least-squares problem with constraints, wherethe objective functional measures violation of some interface conditions. The local con-straints, the Stokes and Biot models, are discretized in time using second-order schemes.Computational algorithms for the least-squares problems are discussed and numericalresults are provided to compare the accuracy and efficiency of the algorithms.

4. Developing efficient IMEX Runge-Kutta methods for nonhydrostaticatmosphere modelsAndrew Steyer, Sandia National Laboratories

Abstract. Nonhydrostatic atmosphere models used for weather forecasting and climateprediction typically require integrating stiff or multirate initial value problems. In suchmodels, horizontally explicit, vertically implicit (HEVI) partitioning strategies are oftenemployed. HEVI partitioning implicitly treats fast terms corresponding to vertical acous-tic wave propagation and explicitly treats the remaining relatively slow terms. In thistalk we develop the IMKG family of implicit-explicit Runge-Kutta (IMEX RK) meth-ods for integrating the HOMME-NH nonhydrostatic atmosphere model. The stability ofIMKG methods is characterized with a test equation specific to HEVI models. We focuson methods with a large number of explicit stages that maximize their stability relativeto this test equation. The accuracy and efficiency of the IMKG methods is compared toother methods from the literature.

MS1: Advances in numerical methods for multi-physics problems (Part II)





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Talksdetails:

1. High Rayleigh number variational multiscale large eddy simulations ofRayleigh-Benard convectionDavid Sondak, Harvard University

Abstract. Rayleigh-Benard convection (RBC) is a paradigmatic problem in fluid me-chanics and heat transfer, often used as a simplified model for thermal convection. Despitea long history of analysis, there are basic open questions on the nature of heat transport inRBC. Of particular interest is the scaling of the nondimensional heat transport (codifiedas the ratio of total heat transport to conductive heat transport in the Nusselt number(Nu)) with Rayleigh number (Ra). Numerical experiments can provide perspective onthis scaling, but are challenged in the very high Ra regime due to the onset of turbulence.In the present work, we propose a variational multiscale (VMS) formulation for high RaRBC. We perform a number of large eddy simulations of two-dimensional and three-dimensional RBC up to Ra = 1014 and compare Nusselt scaling to data from experimentsand direct numerical simulations. We consider limitations of the present VMS formulationand propose modifications that improve the overall performance and predictive capability.

2. On some complex coupled multi-physics PDE: combining electromag-netics and continuum mechanicsAmnon J Meir, Southern Methodist University

3. Adjoint based a posteriori error analysis for stationary resistive MHDAri Rappaport, University of New Mexico

Abstract. Adjoint-based a posteriori error analysis is a technique for producing ex-act error representations for quantities of interests that are functions of the solution ofsystems of partial differential equations (PDE). In this talk we apply the a posteriorierror analysis to the equations of incompressible resistive magnetohydrodynamics (MHD)approximated with an exact penalty variational formulation [Gunzburger et al]. MHDprovides a continuum level description of conducting fluids in the presence of electromag-netic fields. The MHD system is therefore a multi-physics system, capturing both fluidand electromagnetic effects. Mathematically, The equations of MHD are highly nonlinearand fully coupled, adding to the complexity of the a posteriori analysis. Additionally,there is a stabilization necessary to ensure the so called solenoidal constrant (div B = 0)is satisfied in a weak sense. We present the linearized adjoint system and demonstrateit’s effectiveness on several numerical examples.

4. Highly-scalable Poisson solvers on GPUsPedro Bello-Maldonado, University of Illinois at Urbana-Champaign

Abstract. Minimizing communication is central to realizing high performance for ef-ficient execution of parallel algorithms. Our focus is on reducing the communication inthe execute phase of iterative solvers, with particular attention to GPU-based systems,by exchanging local work for a reduction in the number of global communications. Wedesigned and implemented a hybrid GPU/CPU, range decomposition preconditioner ca-pable of solving a 3D Poisson problem with 133 million unknowns under 1 second using64 GPUs.

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MS1: Advances in numerical methods for multi-physics problems (Part III)





Talksdetails:

1. Discretization of the multi-fluid plasma model using IMEX and mixedcontinuous/discontinuous FEMSean Miller, Sandia National Laboratories

Abstract. Multi-fluid plasma models are used to accurately simulate the various timeand spatial behaviors found in plasmas. Each particle species is treated as a separateelectromagnetically/collisionally-coupled Euler fluid interacting with Maxwell’s equations,which can lead to a challenging implicit system. In this talk we discuss a numericaltechnique for modeling multi-fluid plasmas using mixed continuous and discontinuousGalerkin spatial discretizations and implicit-explicit time integration. Important time andvelocity scales will be identified and leveraged to reduce the complexity of the assemblyand preconditioning of the system with the goal of a fast, scalable treatment of complexphysics.

2. A five-moment multifluid model for partially ionized plasmas with ar-bitrarily many speciesMichael Crockatt, Sandia National Laboratories

Abstract. We briefly describe progress on the development of a general multifluid modelfor simulations of partially-ionized plasmas composed of multiple atomic species. Themodel, which is an extension of (Meier and Shumlak, Physics of Plasmas, 19 (2012)), isintended for computational simulations of classical high-temperature, low-density plasmas,and can be extended to high-energy-density physics (HEDP) applications such as Z-pinchplasmas. The current implementation evolves an arbitrary number of charge states andatomic species (plus electrons) that interact through binary elastic scattering collisions,and ionization and recombination reactions. In addition, charged species are coupled withelectromagnetic fields generated by either a full Maxwell system or a reduced electrostaticapproximation. The mathematical model is discretized by a continuous Galerkin finiteelement approximation that employs algebraic flux correction (AFC) and IMEX timeintegration techniques.

This talk focuses on the general structure of the model and the form of the interactioncoefficients for elastic scattering collisions and ionization/recombination reactions. Wepresent results for verification problems as well as proof-of-principle computations relevantto massive gas injection as a disruption mitigation strategy for tokamak plasmas.

45


3. Invariant domain preserving methods and convex limitingIgnancio Tomas, Sandia National Laboratories

4. On IMEX-AFC continuous finite element methods for visco-resistiveMHDSibusiso Mabuza, Clemson University

Abstract. In this work, a stabilized continuous finite element method for viscous andresistive magnetohydrodynamics is presented. This method is based on nodal variationlimiting for algebraic flux correction schemes for hyperbolic systems. The resistivity andviscosity require the use of implicit time stepping. Thus, a nonlinear solver is used inwhich a Jacobian has to be constructed. With many time steppers, this demands thatthe limiting strategy be sufficiently differentiable, or that an approximate Jacobian beused. To relax this condition, IMEX time steppers are used in which the viscosity andresistivity are treated implicitly and the convection and stabilization are treated explicitly.Thus, fully accurate Jacobians are built resulting in a more robust solver. Some numericalexamples are considered to demonstrate the performance of the method.

MS2: Recent Developments in Numerical Algorithms for PDEs (Part I)

Organizer: S. S. Ravindran, University of Alabama in Huntsville

Description: The rapid growth and diversity of research in science and engineering over the pastdecades has spawned many intellectually challenging and computationally intensivePDE problems to be solved. Despite significant progress made in development of effi-cient computational methods for numerical solution of these problems, many problemsstill remain open. This mini-symposium aims to provide a platform to present recentdevelopments on the novel and efficient numerical methods for solving nonlinear PDEs,enable in-depth discussions on a variety of computational efforts for solving problemsarising in areas of science and engineering from researchers at all stages of their careers.

Talksdetails:

1. High-order multirate time integration for multiphysics PDE systemsDaniel Reynolds, Southern Methodist University

Abstract. Modern multiphysics applications present numerous challenges for legacynumerical time integration methods, including the presence of multiple processes thatact on disparate time scales, and that combine stiff and nonstiff, as well as linear andnonlinear equations. Although when considered in isolation, optimal methods may existfor each component, no single algorithm is typically suitable for the combined problem.As a result, practitioners have historically tackled multiphysics problems using ad-hocoperator-splitting techniques, that typically exhibit low accuracy and have questionablenumerical stability.

In this talk, we focus on our recent work in constructing novel high-order ‘multirate’ timeintegration methods for multiphysics applications. These flexible approaches allow eachphysical process to be treated using optimal algorithms, while simultaneously providinghigh accuracy and robust stability. Specifically, we will discuss our work in constructingfourth-order (and higher) multirate methods.

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2. On the shock-capturing discontinuous galerkin method based on theentropy principleYu Lv, Missisippi State University

Abstract. Over recent years a set of high-order discontinuous schemes have graduallyemerged as a new cornerstone for enabling high-fidelity CFD applications. The discontin-uous Galerkin (DG) method, as a representative, has been successfully applied to a num-ber of challenging problems and demonstrated superior capabilities over the conventionalfinite-different and finite-volume schemes. Specifically, DG method is able to providehigh-order discretization on unstructured meshes, utilizes a compact discretization, andis well suited for advanced refinement strategies. However, it has been recognized thathigh-order DG approximations suffer robustness issues when applied to solving nonlinearconservation laws. These nonlinear numerical instabilities may arise from physical discon-tinuities, geometrical singularities, and under-resolved turbulence structures. To addressthese issues, the present study is concerned with the development of a realizable and sta-ble high-order DG method, by embedding the entropy principle to the discretization andthereby imposing physical-constraints on local-cell solution representations. After outlin-ing the mathematical formulation and the proof of stability, the performance of the novelDG method is evaluated by considering a series of test cases involving shocks, turbulence,and chemical reaction.

3. Predictor/corrector adaptive mesh refinement for some nonlinear finiteelement problemsTimo Heister, Clemson University

Abstract. Several different Finite Element discretizations of nonlinear problems ex-hibit mesh-dependent solutions and therefore, require care when handling adaptive meshrefinement within a nonlinear iteration.

We look at two specific examples. First, we discuss crack propagation in an elastic mediumusing a phase field approach. The cracks can grow with arbitrary speed and have to beresolved with a certain maximum mesh size. Second, long-term tectonic deformations inEarth require the simulation of nonlinear elasto-visco-plastic materials. Common strate-gies produce solutions that are strongly resolution dependent. Specifically, the width andangle of shear bands in the solution are not robust.

In both cases, standard discretizations lead to different behavior with mesh refinementprohibiting the usage of adaptive mesh refinement. We present a predictor-correct meshrefinement strategy within the nonlinear iteration to provide a solution to these, andpotentially other, problems. Numerical solutions demonstrate the effectiveness of theproposed scheme.

4. Variable stepsize, variable order methods for PDEsVictor DeCaria, Oak Ridge National Laboratory

Abstract. Variable stepsize, variable order (VSVO) methods have limited impact intimestepping methods in complex applications due to their computational complexityand the difficulty to implement them in an existing code. I will introduce a new familyof implicit, embedded, VSVO methods that require only one BDF solve at each time stepfollowed by adding linear combinations of the solution at a small number of previous timelevels to compute solutions of different order. I will also talk about an implicit/explicitfirst-second order embedded pair based on this idea for the Navier-Stokes equations, andsome partial results on stability and convergence.

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MS2: Recent Developments in Numerical Algorithms for PDEs (Part II)



Talksdetails:

1. New finite difference methods on irregular grids for solving theMaxwell’s equationsYingjie Liu, Georgia Tech

Abstract. This talk is based on a recent joint work with Dr. Xin Wang. We have devel-oped new, simple and efficient second order finite difference methods for solving Maxwell’sequations on non-staggered irregular grids with large CFL numbers (greater than or equalto 1 in one, two or three dimensions). The methods don’t need to compute the local charac-teristic information for the hyperbolic system and are easy to implement on unstructuredmeshes. The schemes can be naturally adapted to the perfectly matched layers (PML) forabsorbing boundaries. BFECC had been applied to schemes for scalar advection equationsto improve their stability and order of accuracy. In this talk similar theoretical results forsystems will be introduced. These results are robust for irregular meshes and for nonlinearequations. We apply BFECC to the central difference scheme (unstable if used along),Lax-Friedrichs scheme or a combination of them for the Maxwell’s equations and obtainsecond order accurate schemes with large CFL numbers. The method is further applied toschemes based on the least-squares linear interpolation on non-orthogonal, non-staggeredirregular grids to obtain second order stabilized versions. Numerical examples are givento demonstrate the robustness of the new schemes.

2. A supermesh method for computing solutions to the Stefan problemYang Liu, Florida State University

Abstract. In previous work by the speaker, a novel supermesh method was devel-oped for computing solutions to the multimaterial heat equation in complex stationarygeometries. In present work, the speaker will discuss a novel supermesh algorithm forcomputing solutions to the Stefan problem involving complex deforming geometries. Thesupermesh is established by combining the structured rectangular grid and the piecewiselinear interfaces reconstructed by the moment-of-fluid method. The temperature diffusionequation with Dirichlet boundary at the interfaces is solved by the presenters’ linear ex-act multi-material finite volume method upon the supermesh. The interface propagationequation is resolved by using the unsplit cell-integrated semi-Lagrangian method. Thelevel set method is also coupled during this process in order to assist in the initializationof the (transient) provisional velocity field. The presenters’ method is validated on bothcanonical and challenging benchmark tests. Algorithm convergence results based on gridrefinement are reported. It is found that the new method approximates solutions to theStefan problem efficiently, compared to traditional approaches, due to the localized finitevolume approximation stencil derived from the underlying supermesh. The new kind ofsupermesh approach opens the door for solving many complex deforming boundary prob-lems in which the method has the efficiency properties of a body fitted mesh combinedwith the robustness of a “cut-cell” (a.k.a. “embedded boundary” or “immersed”) method.

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3. A C0 interior penalty method for the phase field crystal equationnAmanda Diegel, Mississippi State University

Abstract. We present a C0 interior penalty method for the phase field crystal equationusing a convex-splitting time discretization. We demonstrate that the numerical schemeis unconditionally energy stable and uniquely solvable. We furthermore benchmark ourmethod against numerical experiments previously established in the literature.

4. Supersonic Euler and magnetohydrodynamic flow past conesIan Holloway, Wright State University

Abstract. The Euler and Ideal Magnetohydrodynamic equations are presented subjectto the assumption of conical invariance. With this assumption, the systems reduce to be-ing defined entirely on the surface of a sphere. This two dimensional problem is simpler toanalyze and less computationally expensive to solve numerically, while still providing valu-able insight into the full three dimensional flow field. The most well known investigationinto conical flows is that of Taylor and Maccoll who considered flow past circular cones atzero angle of attack. That work has now been built upon to consider cones of arbitrarycross section at different angles of attack and angles of roll. A challenge associated withthis type of flow is that the two dimensional domain is curved, which must be accountedfor using tools from tensor calculus. In order to solve the resulting system of equationsnumerically, special care must be taken to derive discrete source terms analogous to theChristoffel symbols. Such source terms are described, and a numerical scheme involvingthem is demonstrated. The numerical scheme is a member of the family of central schemesand therefore does not rely on a costly Riemann solver.

MS2: Recent Developments in Numerical Algorithms for PDEs (Part III)



Talksdetails:

1. DG methods for nonlinear wave equationsThomas Hagstrom, Southern Methodist University

Abstract. We describe the construction of energy-based DG methods for nonlinear waveequations in second order form. These generally follow directly from the Lagrangian ofthe system and the introduction of a second set of variables including the time derivatives.The general specification is overdetermined, and we show how to produce a convenientwell-determined system out of it in special cases, including all semilinear equations. Someexamples involving the sine-Gordon equation will be used to illustrate the method’s per-formance. In addition, second order wave equations can develop various types of singu-larities, and we will discuss some ideas for the numerical approximation of these singularsolutions.

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2. Robust training and initialization of deep neural networks: an adaptivebasis viewpointMamikon Gulian, Sandia National Laboratories

Abstract. Motivated by the gap between theoretical optimal approximation rates ofdeep neural networks (DNNs) and the accuracy realized in practice, we seek to improvethe training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to novelinitializations and a hybrid least squares/gradient descent optimizer. We provide analysisof these techniques and illustrate via numerical examples dramatic increases in accuracyand convergence rate for benchmarks characterizing scientific applications where DNNsare currently used, including regression problems and physics-informed neural networksfor the solution of partial differential equations.

3. Discontinuous Galerkin methods for an elliptic state-constrained opti-mal control problemYi Zhang, University of North Carolina at Greensboro

Abstract. Problems of partial differential equation (PDE)-constrained optimizationarise in many applications and has recently received a significant attention. In this talk,we will briefly introduce C0 interior penalty methods and their applications to solve anelliptic distributed optimal control problem with state constraints and Neumann boundarycondition. Both a priori and a posteriori analysis will be discussed. We will also presentnumerical results to gauge the performance of the proposed methods.

4. Scalable computation of matrix functions for nonlinear PDEs throughasymptotic analysis of block Krylov projectionJames Lambers, University of Southern Mississippi

Abstract. Exponential propagation iterative (EPI) methods provide an efficient ap-proach to solving large stiff systems of ODEs arising from nonlinear PDEs. However, thebulk of the computational effort in these methods is due to products of matrix function-sand vectors, which can become very costly at high resolution due to an increase in thenumber of Krylov projection steps needed to maintain accuracy. In this presentation,EPI methods are modified by using Krylov subspace spectral (KSS) methods, insteadofstandard Krylov projection methods, to compute products of matrix functions and vec-tors. Numerical experiments show that this modification causes the number of Krylovprojection steps to become bounded independently of the grid size, thus dramaticallyimprovingefficiency and scalability.

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MS3: Recent Developments of Numerical methods for Fluid Flows and Ap-plications (Part I)

Organizer: Thi-Thao-Phuong Hoang, Auburn University

Description: Numerical simulation of fluid flows is a topic of great interest with a wide range ofapplications. The goal of this minisymposium is to bring together mathematicians andscientists to present cutting-edge research on efficient numerical schemes, their analysisand application to the numerical solution of various problems in fluid dynamics.

Talksdetails:

1. Weighted least-squares finite element methods for viscoelastic fluid flowsHyesuk Lee, Clemson University

Abstract. A least-squares (LS) finite element method with an adaptive mesh approachis proposed for Giesekus viscoelastic 4-to-1 contraction flow problems. We consider theweighted LS method on uniform and adaptive meshes for the Newton linearized vis-coelastic problem, where adaptive grids are automatically generated by the least-squaressolutions. We use a residual-type a posteriori error estimator to adjust weights in theLS functional and compare the convergence behavior of adaptive meshes generated usingdifferent grading functions. Numerical results demonstrate that the adaptive LS methodconverges at least linearly when equal-order linear interpolation functions are used for allvariables, which agrees with the theoretical a priori error estimate.

2. Accelerating solvers for degenerate problemsSara Pollock, University of Florida

Abstract. The efficient solution of systems of nonlinear equations is an important toolfor the modeling of physical phenomena. Accelerating fixed-point iterations for nondegen-erate systems of equations is now largely understood, but the theory behind acceleratingsolves for degenerate elliptic problems has largely yet to be explored. In this talk we willconsider a solution technique based on adaptive parameter selection within an extrapo-lation technique known as Anderson acceleration. Examples will include finite elementdiscretizations of the 𝑝-Laplacian for both 1 < 𝑝 < 2 and 𝑝 > 2.

For 1 < 𝑝 < 2, the equation is singular, and adaptive depth selection allows the acceler-ated algorithm to converge with greater efficiency than either a fixed-depth acceleratedor standard fixed-point iteration. For 𝑝 > 2, the problem is degenerate, and adaptivedepth selection allows the efficient solution of problems for which the standard fixed-pointiteration fails to converge. In both cases, the additional use of adaptive damping based onthe success of the acceleration algorithm at each iteration can improve the performanceof the method.

3. Efficient ensemble algorithms for numerical approximation of stochasticStokes-Darcy equationsNan Jiang, Missouri University of Science and Technology

Abstract. This talk will present efficient ensemble algorithms for fast computation ofmultiple realizations of the stochastic Stokes-Darcy model with a random hydraulic con-ductivity tensor. The algorithms result in a common coefficient matrix for all realizationsmaking solving the linear systems much less expensive while maintaining comparable accu-racy to traditional methods that compute each realization separately. Numerical exampleswill be presented to demonstrate the efficiency of the algorithm.

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4. A posteriori error estimates for weak Galerkin methods for Stokes equa-tions on polygonal meshesLin Mu, University of Georgia

Abstract. In this talk, we shall introduce a simple posteriori error estimate of the weakGalerkin (WG) finite element method. This residual type a posteriori error estimate canbe applied to general polygonal meshes or meshes with hanging nodes. The reliability andefficiency of the designed error estimator have been proved and validated. These resultsdemonstrate the effectiveness of the adaptive mesh refinement guided by the proposederror estimator.

MS3: Recent Developments of Numerical methods for Fluid Flows and Ap-plications (Part II)

Organizer: Thi-Thao-Phuong Hoang, Auburn University


Talksdetails:

1. Maximum bound principles for a class of semilinear parabolic equationsand exponential time differencing schemesLili Ju, University of South Carolina

Abstract. In this talk, we consider a practically desirable property for a class of semi-linear parabolic equations of the abstract form 𝑢𝑡 = 𝐿𝑢 + 𝑓 [𝑢] with 𝐿 being a lineardissipative operator and 𝑓 being a nonlinear operator in space, namely a time-invariantmaximum bound principle, in the sense that the time-dependent solution 𝑢 preserves forall time a uniform pointwise bound imposed by its initial and boundary conditions.Wefirst study an analytical framework for some sufficient conditions on 𝐿 and 𝑓 that lead tosuch a maximum bound principle for the time-continuous dynamic system of infinite orfinite dimensions. Then we design suitable exponential time differencing approach witha properly chosen generator of the semigroup to develop first- and second-order accuratetemporal discretization schemes that satisfy the maximum bound principle uncondition-ally in the time-discrete setting. Error estimates of the proposed schemes are derived alongwith their energy stability. Extensions to vector- and matrix-valued systems are also dis-cussed. We demonstrate that the abstract framework and analysis techniques developedhere offer an effective and unified approach to study the maximum bound principle ofthe abstract evolution equation that cover a wide variety of well-known models and theirnumerical discretization schemes. Numerical experiments are also carried out to verifythe theoretical results.

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2. Exponential integrators for meteorological equationsVu Thai Luan, Mississippi State University

Abstract. Development of efficient, stable, and accurate time integration techniqueshas been a central issue of meteorological models over the past 70 years. This is primarilydue to the existence of vastly differing time-scales (known as stiffness) in atmosphericphenomena, ranging from a relatively slow advection to very fast gravity waves, whichposes a major challenge for time integration techniques. In this talk, we propose the useof exponential time integration methods, which are designed for large-scale stiff systems.They are fully explicit, in that they do not require iterative nonlinear solvers, and showunconditional linear stability. For the accuracy and efficiency purposes, we identify thethree efficient schemes of orders 4 and 5 based on a suite of challenging tests problems per-formed with the shallow water/compressible Euler models on a geodesic icosahedral grid.Moreover, we propose an efficient modification of one of state-of-the-art algorithms for theimplementation of exponential integrators. Altogether, this allows the proposed schemesenable accurate solutions at much longer time-steps than the semi-implicit schemes whichhave been widely used, proving more efficient as the desired accuracy decreases or as theproblem nonlinearity increases.

3. Geometric Multigrid for massively parallel, adaptive, large scale StokesflowTimo Heister, Clemson University

Abstract. We present a large scale, parallel geometric multigrid method for Stokesflow on adaptively refined meshes. The motivation is the simulation of convection in theEarth’s mantle. The governing equations are solved using the Finite Element method onadaptively refined meshes, which allows us to resolve features at high resolution, withoutintractable computational cost.

Nevertheless, linear systems can become quite large (100+ million unknowns), so effi-cient, parallel solvers are necessary. We are implementing massively-parallel, matrix-free,geometric Multigrid solvers to solve the Stokes part of the governing equations.

The solver is implement in the open source mantle convection code ASPECT that is builton the open source deal.II finite element library. We will show benchmark results thatconfirm far better performance and scalability compared to the algebraic multigrid solversbuilt on assembled matrices, that were used in ASPECT until now. We can show goodscalability to 100,000+ cores and 100s of billions of unknowns.

4. Space-time domain decomposition methods for Stokes-Darcy couplingThi-Thao-Phuong Hoang, Auburn University

Abstract. We study decoupling iterative algorithms based on domain decompositionfor the time-dependent nonlinear Stokes-Darcy model, in which different time steps canbe used in the flow region and in the porous medium. The coupled system is formulatedas a space-time interface problem based on the transmission conditions at the interfacebetween the two regions. The nonlinear interface problem is then solved by a nestediteration approach which involves, at each Newton iteration, the solution of a linearizedinterface problem and, at each Krylov iteration, parallel solution of time-dependent lin-earized Stokes and Darcy problems. Consequently, local discretizations in both space andtime can be used to efficiently handle multiphysics systems with discontinuous param-eters. Numerical results with nonconforming time grids are presented to illustrate theperformance of the proposed methods.

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MS4: Recent Developments in Nonlocal Continuum Modeling (Part I)

Organizers: James Scott, University of Tennessee

Pablo Seleson, Oak Ridge National Laboratory


Talksdetails:

1. Nonlocal brittle fracture modeling with applied traction forcesRobert Lipton, Louisiana State University

Abstract. A simple nonlocal field theory of peridynamic type is applied to model brittlefracture. The nonlocal fracture evolution with a nonlocal applied force is seen to convergein the limit of vanishing nonlocality to classic plane elastodynamics with a running crackgenerated by applied traction boundary conditions. The kinetic relation for the crack isrecovered directly from the nonlocal model in the limit of vanishing nonlocality. We carryout our analysis for a single crack in a plate subject to mode one loading. The convergenceis corroborated by numerical experiments.

2. Overall equilibrium in the coupling of peridynamics and classical con-tinuum mechanicsPablo Seleson, Oak Ridge National Laboratory

Abstract. Peridynamics is a nonlocal reformulation of classical continuum mechanics,based on integro-differential equations, suitable for material failure and damage simula-tion. Peridynamics naturally allows modeling of evolving cracks (i.e. spatial discontinu-ities) in a material, because corresponding constitutive relations lack spatial differentiabil-ity requirements, as opposed to the classical PDE-based theory. However, peridynamicsis more computationally expensive than its classical counterpart. Coupling peridynamicsand classical continuum mechanics is an effective way to attain suitable crack propaga-tion representations while remaining computationally tractable. In this presentation, wewill address the problem of the overall equilibrium in the coupling of peridynamics andclassical continuum mechanics. We will provide an analysis of the origin of out-of-balanceforces in coupled configurations and propose possible ways to reduce them, supported bynumerical examples.

3. Regularity of solutions to nonlinear nonlocal equations and systems incontinuum mechanicsJames Scott, University of Tennessee

Abstract. We show self-improving inequalities of solutions to nonlocal continuum mod-els. We consider a variety of nonlocal equations and systems for which a variationalprinciple holds, and show that in each context weak solutions satisfy a reverse Hölder’sinequality. This permits the application of a Gehring-type lemma, which in turn demon-strates that weak solutions enjoy both improved differentiability and improved integra-bility. Examples of such nonlocal equations and systems for which these results holdinclude strongly-coupled nonlocal systems related to bond-based peridynamics, the Euler-Lagrange equation for nonlocal double phase integrals and Dirichlet-to-Neumann opera-tors associated to the Navier-Lamé system of classical elasticity for isotropic materials.The techniques used to obtain a reverse Hölder’s inequality vary depending on the equa-tion considered, and a summary of said techniques will be presented for each example.

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4. New families of fractional PDEs arising from fractional calculus of vari-ationsMitchell Sutton, University of Tennessee

Abstract. In this talk we shall present two new families of fractional PDEs obtainedas Euler-Lagrange equations of fractional calculus of variations problems. Several newfractional differential operators will be introduced, including the fractional 𝑝-Laplacian,Laplacian, and Neumann boundary operator. In each family of problems, we considerone-sided differentiation as well as differentiation in each direction. The first family ofproblems connects minimization problems with prescribed boundary conditions to asso-ciated fractional PDEs via the calculus of variations. The second family of problemsestablishes the connection between minimization problems with natural boundary condi-tions and fractional PDEs with Neumann boundary data. We prove the existence anduniqueness of weak solutions in the newly developed fractional Sobolev space(s). We alsoconsider fractional PDEs for which there is no associated minimization problem. In ad-dition to proving existence and uniqueness of solutions, we discuss the issue of choosingappropriate initial conditions and our interpretation of an initial value problem.

MS4: Recent Developments in Nonlocal Continuum Modeling (Part II)




Talksdetails:

1. Fractional order viscoelastic modeling and Bayesian uncertainty analysisof elastomers and auxetic foamsWilliam Oates, Florida State University

Abstract. We will discuss connections between fractional order viscoelastic behaviorand fractal structure of elastomers and polymeric foams. A set of governing equationswill be introduced using maximizing entropy methods under material constraints andthen applied to fractional viscoelasticity in soft elastomers and auxetic (negative Pois-son) foams. A set of relations that connect fractal geometric structure, spectral vibrationmode relations, and fractional viscoelastic order are shown to be related. We validatethe theory through a series of experiments. These experiments include measurements offinite deformation stress-strain, infrared measurements of heat diffusion, and microscopyimages. These individual measurements lead to new insight on connections between frac-tal structure and fractional properties. A separate set of experiments on auxetic foamsare presented and compared to a model that accommodates negative and nonlinear Pois-son effects super-imposed with fractional viscoelasticity. In all experiments and modelcomparisons, Bayesian uncertainty quantification is used to quantify uncertainty in thefractional order parameters.

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2. Fractional optimal control problems with state constraints: algorithmand analysisDeepanshu Verma, George Mason University

Abstract. Motivated by several applications in geophysics and machine learning, in thistalk, we introduce a novel class of optimal control problems with fractional pdes. Themain novelty is due to the obstacle type constraints on the state. The analysis of thisproblem has required us to create several new, widely applicable, mathematical tools suchas characterization of dual of fractional Sobolev spaces, regularity of pdes with measure-valued datum. We have created a Moreau-Yosida based algorithm to solve this class ofproblems. We establish convergence rates with respect to the regularization parameter.Finite element discretization is carried out and a rigorous convergence of the numericalscheme is established. Numerical examples confirms our theoretical findings.

3. A convergent monotone scheme for a nonlocal segregation model withfree boundaryXiaochuan Tian, University of Texas at Austin

Abstract. We consider a free boundary problem arising from segregation of two specieswith high competition. One species moves according to the classical diffusion and theother adopts a nonlocal diffusion strategy. Being a fully nonlinear nonlocal model, it ischallenging to design effective ways to compute the solution, especially to capture the freeboundary well. We propose an iterative scheme that constructs a sequence of monotoneviscosity supersolutions that is shown to converge to the viscosity solution (in the senseof Crandall-Lions). The numerical method applies to general domains in all dimensions.Moreover, for simple domains it can be shown that the sequence of supersolutions con-verges with a precise rate. We will shown numerical experiments in the end. This is ajoint work Luis Caffarelli and Irene Gamba.

4. The evolution of scientific collaborations in peridynamicsBiraj Dahal, Clemson University

Abstract. The field of peridynamics currently consists of hundreds of scientists and iscontinually growing. As a relatively young field, it is of interest to study the evolution ofscientific collaborations in peridynamics. Not only will this potentially allow us to under-stand how the peridynamic community has been evolving during the past 20 years, but itmay also provide insights on other similar scientific communities. In this presentation, wewill discuss the evolution of the peridynamics community by studying its collaborationnetwork. In that network, nodes consist of scientists and edges represent collaborationsbetween scientists. We use higher-dimensional network models known as simplicial com-plexes in order to reflect the reality that researchers often collaborate in larger groups.From this network data, we evaluate how the collaborations have grown over time at boththe local level and the global level. We will also examine the present state of the network,determining the most central researchers and communities to the entire field.

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MS4: Recent Developments in Nonlocal Continuum Modeling (Part III)




Talksdetails:

1. A fast numerical method for a state-based PD modelHong Wang, University of South Carolina

2. Convergence studies in meshfree peridynamic wave and crack propaga-tionMarco Pasetto, University of California, San Diego

Abstract. Peridynamics is a nonlocal reformulation of classical continuum mechanicssuitable for material failure and damage simulation. Governing equations in peridynam-ics are based on spatial integration rather than spatial differentiation, allowing naturalrepresentation of material discontinuities such as cracks. A node-based meshfree dis-cretization approach has been demonstrated to be an effective discretization method forlarge-scale engineering simulations, particularly those involving large deformation andcomplex fractures. However, while the convergence of meshfree numerical solutions ofstatic peridynamic problems has been investigated, a robust quantitative assessment ofthe performance of this meshfree method, particularly in fracture scenarios, is lacking Inthis talk, we will discuss recent convergence studies of wave propagation and extensions todynamic crack propagation in meshfree peridynamic simulations, under different choicesof influence functions and integration weights.

3. An RBF quadrature rule approach for solving nonlocal continuum mod-elsIsaac Lyngaas, Oak Ridge National Laboratory

Abstract. Recently nonlocal continuum models have gained interest as alternatives totraditional PDE models due to their capability of handling solutions with discontinuitiesand their ease of modeling anomalous diffusion. The typical approach used for approxi-mating these time-dependent nonlocal integro-differential models is to use finite elementor discontinuous Galerkin methods; however these approaches can be quite computation-ally intensive especially when solving problems in more than one dimension due to theapproximaton of the nonlocal integral. We propose a novel method based on using radialbasis functions to generate accurate quadrature rules for the nonlocal integral appear-ing in the model and then couple these with a finite difference approximation to findthe time-dependent terms. The viability of our method is demonstrated through variousnumerical tests on time dependent nonlocal diffusion, nonlocal anomalous diffusion andnonlocal advection problems in one and two dimensions. In addition to nonlocal problemswith continuous solutions, we modify our approach to handle problems with discontinuoussolutions. We compare some numerical results with analogous finite element results anddemonstrate that for an equivalent amount of computational work we obtain much higherconvergence rates.

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4. Implementation of a parallel MHD FEM FMM solverK. Daniel Brauss, Francis Marion University

Abstract. We discuss a numerical solution to a velocity-current formulation of the mag-netohydrodynamics (MHD) equations. The velocity-current formulation is an integro-differential system involving Biot-Savart’s Law for the magnetic field. The system ofpartial differential equations is approximated using a Picard iteration and a mixed finiteelement method (FEM) in primitive variables. The Biot-Savart integral is determinedusing a parallel, multi-level fast multipole method (MLFMM) that wraps into the deal.iilibrary. The matrix system is solved using GMRES and a Schur-complement precondi-tioner.

MS5: Modeling, Analysis, Approximation and Parameter Identification ofFractional PDEs and Nonlocal Models (Part I)

Organizers: Hong Wang, University of South Carolina

Yong Zhang, University of Alabama

Xiangcheng Zheng, University of South Carolina

Bingqing Lu, University of Alabama

Description: Fractional partial differential equations (FPDEs) were shown to provide a more ap-propriate modeling tool of challenging phenomena including anomalous transport, andlong range time memory or spatial interactions, which exhibit power-law decayingtails, than integer-order PDEs, which are characterized by Gaussian type symmetricand exponentially decaying tails. Nevertheless, FPDEs present new mathematical andnumerical difficulties that are not common in the context of integer-order PDEs and sorequire rigorous modeling, numerical and mathematical analysis. This minisymposiumcovers modeling, mathematical and numerical analysis, numerical approximations andcomputation, parameter identification and application of FPDEs and nonlocal models.

Talksdetails:

1. Lagrangian approximation of vector fractional diffusion with reactionsin bounded domainsYong Zhang, University of Alabama

2. Mathematical modeling of variable-order fractional differential equa-tionsHong Wang, University of South Carolina

3. Self-Singularity capturing and fast IMEX schemes for nonlinear stochas-tic fractional differential equationsJorge Suzuki, Michigan State University

4. Fast Petrov-Galerkin spectral methods for fixed-to-distributed FPDEsin high dimensionsMehdi Samiee, Michigan State University

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MS5: Modeling, Analysis, Approximation and Parameter Identification ofFractional PDEs and Nonlocal Models (Part II)

Organizers: Hong Wang, University of South Carolina

Yong Zhang, University of Alabama

Xiangcheng Zheng, University of South Carolina

Bingqing Lu, University of Alabama

Description: Fractional partial differential equations (FPDEs) were shown to provide a more ap-propriate modeling tool of challenging phenomena including anomalous transport, andlong range time memory or spatial interactions, which exhibit power-law decayingtails, than integer-order PDEs, which are characterized by Gaussian type symmetricand exponentially decaying tails. Nevertheless, FPDEs present new mathematical andnumerical difficulties that are not common in the context of integer-order PDEs and sorequire rigorous modeling, numerical and mathematical analysis. This minisymposiumcovers modeling, mathematical and numerical analysis, numerical approximations andcomputation, parameter identification and application of FPDEs and nonlocal models.

Talksdetails:

1. New Characterizations of Sobolev and Potential SpacesJames Scott and Tadele Mengesha, University of Tennessee

Abstract. We show that a class of spaces of vector fields whose semi-norms involvethe magnitude of "directional" difference quotients is in fact equivalent to the class offractional Sobolev spaces. The equivalence can be considered a Korn-type characterizationof fractional Sobolev spaces. We additionally show that the class of vector-valued Besselpotential spaces can be characterized by a Marcinkiewicz-type integral that that is -pointwise - smaller than the classical Marcinkiewicz integral, and does not resemble otherclasses of potential-type integrals found in the literature. In applications, these results areused to better understand spaces of vector fields associated to a strongly coupled systemof nonlocal equations related to a continuum model of peridynamics.

2. Fractional advection-dispersion-reaction equation (f-ADRE) to capturenitrate fate and transport in soilBingqing Lu and Yong Zhang, University of Alabama

3. Analysis and numerical approximations of variable-order time andspace-time fractional diffusion equationsXiangcheng Zheng, University of South Carolina

Abstract. We proved the wellposedness of variable-order time and space-time fractionaldiffusion equations and the regularity of their solutions. Optimal-order finite elementapproximation was presented and analyzed. Numerical experiments were carried out todemonstrate the theoretical results.

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4. Analysis and numerical inversion of the inverse problem of determiningthe variable fractional order in variable-order time-fractional diffusionequationsYiqun Li, University of South Carolina

Abstract. Variable-order time-fractional diffusion equations provide competitive model-ing capabilities of challenging phenomena including anomalously subdiffusive transport ofsolutes in heterogeneous porous media and memory effect as constant order time-fractionaldiffusion equations do, and eliminate the nonphysical singularity of the solutions of the lat-ter near the initial time. Moreover, they occur naturally in many applications. We studythe initial-boundary value problem of a variable-order time-fractional diffusion equationand prove the uniqueness of determining the variable order in the problem, from the ob-servations of its solution on a sufficiently small open rectangle over a sufficiently smalltime interval. We also develop the Levenberg-Marquardt (L-M) Algorithm to numericallyinvert the variable order and numerical experiments show that the proposed L-M methodis quite feasible.

MS6: Recent Developments and Applications in Computational Biology(Part I)

Organizers: Shan Zhao, University of Alabama

Xinfeng Liu, University of South Carolina

Description: Due to the rapid developments of mathematical models and computational algorithms,computational biology has become a significant approach to understand the biologicalphenomena. This minisymposium will focus on continuous type math models includingPDEs and ODEs, which help to better understand biological experiments and predictmore information. A variety of biological applications at multiple scales, such as atmolecular, cell and tissue levels, will be considered. Emphasis will be placed not onlyon mathematical theories and methods, but also on biological simulations and softwaredevelopments closely integrated with experiments.

Talksdetails:

1. A Newton-like method for solving the Poisson-Boltzmann equation andits implementation in the DelPhi suiteChuan Li, West Chester University of Pennsylvania

Abstract. The DelPhi Suite is a popular finite difference solver adopted world-widely forsolving the Poisson-Boltzmann equation (PBE) and calculating the electrostatic potentialand energies on live molecules and proteins immersed in water due to its efficiency andflexibility. In the DelPhi Suite, the discrete linear system of the linearized PBE (LPBE)is solved by a Successive Over Relaxation (SOR) method, with many sophisticated im-plementations to improve computational efficiency, while the nonlinear PBE (NPBE) issimply solved by a nonlinear relaxation method. However, it is known that divergencemay occur when solving the NPBE on some difficult cases when highly charged atomsare close to the surfaces and the calculated potential at a grid in water passing certainthreshold. This motivates us to develop a new Newton-like method that will not only im-prove the stability for the NPBE, but also inherit computational techniques implementedin current DelPhi suite for maintaining the efficiency of the SOR algorithm. This talkpresents this newly developed Newton-like method, as well as experiments to demonstrateits performance.

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2. Micro-macro coupling of fluid dynamics in complex fluidPaula Vasquez, University of South Carolina

Abstract. Viscoelastic materials are characterized by the coupling of microstructuralchanges to macroscale deformations. In this talk, we discuss an elastic dumbbell modelthat leverages the parallel processing power of High Performance Computing (HPC)Graphics Processing Units (GPUs) to create a unique micro-macro scale driven designwhich incorporates the nonlinear nature of viscoelastic responses as well as the stochasticprocesses which describe the breaking and reforming of entanglements in the underly-ing microscopic network. The model allows a full reconstruction of the microstructure-flow coupling thereby creating a platform with the ability to investigate how microscopicchanges affect macroscopic responses.

3. Mathematical modeling reveals a noncanonical feedback between mes-senger RNA and microRNATian Hong, University of Tennessee

Abstract. Systems level feedbacks are crucial mechanisms for cell fate decisions andtheir underlying physiology. Gene regulatory positive feedbacks, which normally dependstranscriptional control of gene expression, endow robustness and irreversibility to thesedecisions through the formation of bistable switches. A common utility of transcriptionalfeedbacks is the formation of sharp tissue boundary arising from cell fate decisions in fac-ing ambiguous positional signals. We found that a sharp boundary between two adjacentgroups of motor neuron subtypes in the developing spinal cord does not involve canonicaltranscriptional feedback between two fate determining transcriptional factors, Hoxa5 andHoxc8. We hypothesized that microRNA (miRNA) mediated post-transcriptional controlis responsible for a noncanonical feedback mechanism. We built a series of mathematicalmodels describing elementary biochemical reactions involving Hox mRNA and miRNA,and we found that a wide range of biologically plausible parameters generate bistableswitches with only post-transcriptional interactions. Using mathematical analysis, weprovided an intuitive explanation for this feedback mechanism which depends on reactionnetworks that cannot be directly translated to influence networks commonly used to de-scribe feedback controls. This previously underappreciated feedback may be a widespreadmechanism for cell fate decisions and tissue patterning.

4. Boundary conditions and numerical techniques for catching the Gaus-sian curvature in hybrid modeling of protein-membrane interactionsYongcheng Zhou, Colorado State University

Abstract. An hybrid modeling of membrane curvature induced by protein embeddinga tricky problem is the determination of boundary conditions on far boundary and on theprotein-membrane interfaces. In this talk I will discuss the physically justifiable modelingof the membrane curvature on these boundaries and the solution of the related PDEsusing a weak Galerkin method.

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MS6: Recent Developments and Applications in Computational Biology(Part II)

Organizers: Shan Zhao, University of Alabama

Xinfeng Liu, University of South Carolina

Description: Due to the rapid developments of mathematical models and computational algorithms,computational biology has become a significant approach to understand the biologicalphenomena. This minisymposium will focus on continuous type math models includingPDEs and ODEs, which help to better understand biological experiments and predictmore information. A variety of biological applications at multiple scales, such as atmolecular, cell and tissue levels, will be considered. Emphasis will be placed not onlyon mathematical theories and methods, but also on biological simulations and softwaredevelopments closely integrated with experiments.

Talksdetails:

1. A Hybrid model for simulating sprouting angiogenesis in biofabricationYi Sun, University of South Carolina

Abstract. We present a 2D hybrid model to study sprouting angiogenesis of multi-cellular aggregates during vascularization in biofabrication. This model is developed todescribe and predict the time evolution of angiogenic sprouting from endothelial spheroidsduring tissue or organ maturation in a novel biofabrication technology–bioprinting. Herewe employ typically coarse-grained continuum models (reaction-diffusion systems) to de-scribe the dynamics of vascular-endothelial-growth-factors, a mechanical model for theextra-cellular matrix based on the finite element method and couple a cellular Potts modelto describe the cellular dynamics. The model can reproduce sprouting from endothelialspheroids and network formation from individual cells.

2. French ducks in the heart: canard analysis can explain voltage-drivenearly afterdepolarization phenomena in cardiac cellsJoshua Kimrey, Florida State University

Abstract. Early afterdepolarizations (EADs) are pathological voltage fluctuations thatcan occur during a cardiac action potential and are a potent source of potentially fatalarrhythmias. Recent mathematical works have revealed that voltage-driven EADs in min-imal models are canard-induced mixed-mode oscillations whose properties are mediatedby the rate at which these cells are paced. In this talk, we analyze the mechanisms forthe pacing-induced generation of different EAD behaviors in a reduced four-dimensionalLuo-Rudy I model using fast-slow analysis. While previous explanations for EADs inthis model have required manipulation of the underlying multi-timescale structure, ourapproach does not and we find that the canard mechanism persists in generating EADs inthis context; we also find that the canard mechanism gives a more complete explanationfor the onset and properties of the EADs induced (e.g., EAD amplitude and number).In addition, we find that the canards play an essential role in producing a rich set ofbehaviors–some of which have been observed in experiments–which have not been seenin minimal models. These behaviors include pacing-induced termination of EADs andbistability between standard and EAD-containing action potentials at fixed pacing rates.Finally, we show that this bistability can lead to hysteretic transitions between standardand arrhythmogenic action potentials under sufficiently slow oscillations in the pacingrate.

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3. Mathematical modeling, computation and experimental investigation ofdynamical heterogeneity in breast cancerXinfeng Liu, University of South Carolina

Abstract. Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) area highly tumorigenic cell type found in developmentally diverse tumors that are believedto be resistant to standard chemotherapeutic drugs and responsible for tumor recurrence.Thus understanding the tumor growth kinetics is critical for development of novel strate-gies for cancer treatment. For this talk, I shall introduce mathematical modeling to studyHer2 signaling for the dynamical interaction between cancer stem cells (CSCs) and non-stem cancer cells, and our findings reveal that two negative feedback loops are critical incontrolling the balance between the population of CSCs and that of non-stem cancer cells.Furthermore, the model with negative feedback suggests that over-expression of the onco-gene HER2 leads to an increase of CSCs by regulating the division mode or proliferationrate of CSCs.

4. A regularization approach for biomolecular electrostatics involving sin-gular charge sources and diffuse interfacesShan Zhao, University of Alabama

Abstract. Calculations of electrostatic potential and solvation energy of macromoleculesare essential for understanding the mechanism of many biological processes. In the im-plicit solvent Poisson-Boltzmann (PB) models, the macromolecule and water are modelledas two-dielectric media with an interface, and singular charge sources are expressed interms of Dirac delta functions. For sharp interface PB models, singular charges could beanalytically treated by fundamental solutions or regularization methods. However, no an-alytical treatment is known in the literature in case of a diffuse interface of complex shape.This work reports the first such regularization method for diffuse interface PB models,by representing the Coulomb potential analytically via Green’s functions to account forsingular charges. The other component, i.e., the reaction field potential, then satisfiesa regularized PB equation with a smooth source and the original elliptic operator. Theregularized equation can then be simply solved by any numerical method. The proposedregularization is validated by comparing with a semi-analytical quasi-harmonic methodfor a spherical geometry. Based on a simple procedure for constructing diffuse interfacesin complex geometries, the new algorithm is benchmarked by calculating free energies forvarious proteins.

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MS7: Classic and Deep Learning Methods for Data Driven Models (Part I)

Organizers: Zhu Wang, University of South Carolina

Lili Ju, University of South Carolina

Description: Modern sensor technology and data acquisition capability have led to the explosiveproduction of digital data and information. Data-driven approaches based on modelreduction methods or machine learning techniques are powerful tools for extractingimportant characteristics and essential representations from the massive data, affect-ing every branch of science and social life with unprecedented impact. Although deeplearning has achieved tremendous successes in many areas such as computer visionand speech recognition, challenges still exist in many scientific and engineering areas.This mini-symposium will focus on recent advances in data-driven approaches, includ-ing classic dimensionality reduction methods and emerging deep learning algorithms,together with their applications in scientific research and engineering.

Talksdetails:

1. Information Newton’s flow: second-order optimization method in prob-ability spaceWuchen Li, University of California, Los Angeles

Abstract. Markov chain Monte Carlo (MCMC) methods nowadays play essential rolesin machine learning, Bayesian sampling problems, and inverse problems. To acceleratethe MCMC methods, we formulate a high order optimization framework for acceleratedthem. It can be viewed as Newton’s flows in probability space with information met-rics, named information Newton’s flows. Here two information metrics are considered,including both the Fisher-Rao metric and the Wasserstein-2 metric. Several examplesof information Newton’s flows for learning objective/loss functions are provided, such asKullback-Leibler (KL) divergence, Maximum mean discrepancy (MMD), and cross en-tropy. The asymptotic convergence results of proposed Newton’s methods are provided.A known fact is that classical MCMC methods, such as overdamped Langevin dynam-ics, correspond to Wasserstein gradient flows of KL divergence. Extending this fact toWasserstein Newton’s flows of KL divergence, we derive Newton’s Langevin dynamics.We provide examples of Newton’s Langevin dynamics in both one-dimensional space andGaussian families. For the numerical implementation, we design sampling efficient vari-ational methods to approximate Wasserstein Newton’s directions. Several numerical ex-amples in Gaussian families and Bayesian logistic regression are shown to demonstratethe effectiveness of the proposed method

This is based on a joint work with Yifei Wang.

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2. Nonlinear level-sets learning for dimensionality reduction in high-dimensional function approximationGuannan Zhang, Oak Ridge National Laboratory

Abstract. We developed a Nonlinear Level-set Learning (NLL) method for dimension-ality reduction in high-dimensional function approximation with small data. There aretwo major challenges in constructing such predictive models: (a) high-dimensional inputs(e.g., many independent design parameters) and (b) small training data, generated byrunning extremely time-consuming simulations. Thus, reducing the input dimension iscritical to alleviate the over-fitting issue caused by data insufficiency. Existing meth-ods, including sliced inverse regression and active subspace approaches, reduce the inputdimension by learning a linear coordinate transformation; our main contribution is to ex-tend the transformation approach to a nonlinear regime. Specifically, we exploit reversiblenetworks (RevNets) to learn nonlinear level sets of a high-dimensional function and pa-rameterize its level sets in low-dimensional spaces. A new loss function was designed toutilize samples of the target functions’ gradient to encourage the transformed function tobe sensitive to only a few transformed coordinates. The NLL approach is demonstratedby applying it to three 2D functions and two 20D functions for showing the improvedapproximation accuracy with the use of nonlinear transformation, as well as to an 8Dcomposite material design problem for optimizing the buckling-resistance performance ofcomposite shells of rocket inter-stages.

3. Closure learning for nonlinear model reduction using deep residual neu-ral networkXuping Xie, Courant Institute, NYU

Abstract. Developing accurate, efficient, and robust closure models is essential in theconstruction of reduced order models (ROMs) for realistic nonlinear systems, which gen-erally require drastic ROM mode truncations. We propose a deep residual neural network(ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection tofilter the given nonlinear PDE and construct a spatially filtered ROM. This filtered ROMis low-dimensional, but is not closed (because of the system’s nonlinearity). (ii) In the sec-ond step, we use ResNet to close the filtered ROM, i.e., to model the interaction betweenthe resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROMframework, data is used only to complement classical physical modeling (i.e., only in theclosure modeling component), not to completely replace it. We also note that the newResNet-ROM is built on general ideas of spatial filtering and deep learning and is inde-pendent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. Thenumerical experiments for the 1D Burgers equation show that the ResNet-ROM is signif-icantly more accurate than the standard projection ROM. The new ResNet-ROM is alsomore accurate and significantly more efficient than other modern ROM closure models.

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MS7: Classic and Deep Learning Methods for Data Driven Models (Part II)

Organizers: Zhu Wang, University of South Carolina

Lili Ju, University of South Carolina

Description: Modern sensor technology and data acquisition capability have led to the explosiveproduction of digital data and information. Data-driven approaches based on modelreduction methods or machine learning techniques are powerful tools for extractingimportant characteristics and essential representations from the massive data, affect-ing every branch of science and social life with unprecedented impact. Although deeplearning has achieved tremendous successes in many areas such as computer visionand speech recognition, challenges still exist in many scientific and engineering areas.This mini-symposium will focus on recent advances in data-driven approaches, includ-ing classic dimensionality reduction methods and emerging deep learning algorithms,together with their applications in scientific research and engineering.

Talksdetails:

1. Scale-equivariant CNN with decomposed convolutional filtersWei Zhu, Duke University

Abstract. Encoding the scale information explicitly into the representation learned bya convolutional neural network (CNN) is beneficial for many computer vision tasks espe-cially when dealing with multiscale inputs. We study, in this paper, a scaling-translation-equivariant (ST- equivariant) CNN with joint convolutions across the space and the scalinggroup, which is shown to be both sufficient and necessary to achieve ST-equivariant rep-resentations. To reduce the model complexity and computational burden, we decomposethe convolutional filters under two pre-fixed separable bases and truncate the expansion tolow-frequency components. A further benefit of the truncated filter expansion is the im-proved deformation robustness of the equivariant representation. Numerical experimentsdemonstrate that the proposed scaling-translation-equivariant networks with decomposedconvolutional filters (ScDCFNet) achieves significantly improved performance in multi-scale image classification and better interpretability than regular CNNs at a reducedmodel size.

2. Machine learning for missing dynamicsHaizhao Yang, Purdue University

Abstract. This talk presents a general framework for recovering missing dynamicalsystems using available data and machine learning techniques. The proposed frameworkreformulates the prediction problem as a supervised learning problem to approximate amap that takes the memories of the resolved and identifiable unresolved variables to themissing components in the resolved dynamics. We demonstrate the effectiveness of theproposed framework with a theoretical guarantee of a path-wise convergence of the re-solved variables up to finite time and numerical tests on prototypical models in variousscientific domains. While many machine learning techniques can be used to validate theproposed framework, we found that recurrent neural networks outperform kernel regres-sion methods in terms of recovering the trajectory of the resolved components and theequilibrium one-point and two-point statistics. This superb performance suggests thatrecurrent neural networks are an effective tool for recovering the missing dynamics thatinvolves approximation of high-dimensional functions.

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3. Data-driven approaches for parameterized diffusion problemsYuankai Teng, University of South Carolina

Abstract. Model reduction techniques have been successfully developed for simulat-ing parametrized PDE problems, which provides a computationally efficient surrogate inmany-query scenarios such as optimization and real-time controls. Inspired by rapidlygrowing impact of deep learning on scientific and engineering research, we propose a novelneural network, GF-Net, for learning the Green’s functions of linear reaction-diffusionequations in an unsupervised fashion. The proposed method overcomes the challenges forfinding the Green’s functions of the equations on arbitrary domains by utilizing physics-informed approach and the symmetry of the Green’s function. As a consequence, itparticularly leads to an efficient way for solving the target equations. We will discussboth data-driven approaches for parametrized diffusion problem in this talk.

MS8: Theory and Practice of Machine Learning (Part I)

Organizers: Viktor Reshniak, Oak Ridge National Laboratory

Joseph Daws, University of Tennessee Knoxville

Description: The recent explosion of research into artificial intelligence, machine learning, and neuralnetworks across many academic disciplines has led to a gigantic zoo of acronyms andconcepts many of which are variations of some core ideas: modeling, approximation,and optimization. These concepts have been examined extensively by the mathemati-cal and statistical communities. Establishing meaningful connections between mathe-matical and statistical theory to machine learning problems is yielding many positiveresults such as better interpretability of machine learning models, better quantifica-tion of stability and robustness, and improved optimization techniques for trainingneural networks. This minisymposium showcases current research demonstrating newtheoretical and practical understanding of machine learning problems.

Talksdetails:

1. A neural network for solving the Poisson equation with homogeneousboundary conditionsJoseph Daws, University of Tennessee Knoxville

Abstract. Neural networks have been shown to be successful at solving some high-dimensional PDE with boundary conditions. This approach is appealing since the num-ber of network parameters required to obtain an approximation appears to depends lessseverely on dimension than mesh-based or tensor product methods. Existing work employsa penalty term which enforces the boundary condition. We introduce a network archi-tecture which always satisfies homogeneous Dirichlet boundary conditions and considersome numerical examples.

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2. Train like a (Var)Pro: Efficient Training of Neural Networks with Vari-able ProjectionElizabeth Newman, Emory University

Abstract. From image classification to PDE surrogate modeling, the ubiquitousnessof deep neural networks (DNNs) is undeniable. However, developing DNNs is difficult -the model must be highly reliable and must generalize well. Popular stochastic optimiza-tion schemes struggle to obtain the necessary accuracy, particularly for physical applica-tions, and require significant time to train. In the supervised setting, training DNNs canbe posed as a separable, nonlinear least-squares problem aimed at tuning the networkweights. In this talk, we will exploit this separability and apply the method of variableprojection (VarPro) to obtain a reduced optimization problem. With VarPro, we cansolve the reduced optimization problem accurately and efficiently through deterministic,iterative methods (e.g., quasi-Newton) with minimal overhead (e.g., independent of theDNN architecture) while offering more potential for parallel implementations. Throughseveral numerical experiments, we will demonstrate that our VarPro scheme can be imple-mented for any smooth, convex function and can outperform popular stochastic schemes(e.g., ADAM) in terms of accuracy with comparable computational complexity.

3. NLP technique associated learning model for predictive analyticsDon Hong, Middle Tennessee State University

Abstract. In this talk, I’ll briefly introduce a recently developed algorithm called BERTin nature language processing (NPL) and discuss a BERT feature based model for predict-ing the helpfulness scores of online customers reviews, as well as other possible applicationsin predictive analytics.

4. Machine learning for classification and segmentation of lung nodules inCT-scansJerry F. Magnan, Florida State University

Abstract. Lung cancer has the highest mortality rate of all cancers in both men andwomen. Screening for lung cancer, and its early detection, diagnosis, and management,are necessary to significantly improve patient outcomes. The algorithmic detection, char-acterization, and diagnosis of abnormalities found in chest CT scan images can be helpfulto radiologists by providing additional medical information to consider in their assessment.Lung nodule segmentation, i.e., the algorithmic delineation of the lung nodule surface, isa fundamental component of an algorithmic nodule analysis pipeline. We introduce anextension of the standard level set image segmentation method where the velocity func-tion is learned from data via machine learning regression methods (e.g., random forests),rather than a priori designed. Instead, our method employs a set of extracted features tolearn a velocity function that guides the level set evolution from initialization. We referto the method as “level set machine learning” (LSML). We apply the LSML method toimage volumes of lung nodules from CT scans in the publicly available LIDC dataset, anddiscuss our method and its results, which are competitive with many other methods.

We also employ the radiologist-quantified, diagnostically-relevant semantic features (de-fined qualitatively and interpreted subjectively by radiologists) for the lung nodules inthe LIDC dataset, and the radiologists assessment of each nodule’s malignancy, accom-plished via a discrete rating system, along with our derived nodule maximum diameterand volume estimates, to train a linear (logistic regression) and nonlinear (random forests)classifier to determine the potential usefulness of these features for computer-aided diag-nosis (CAD). We discuss the methods employed in our analysis, and the results of thisapproach, which are comparable to those obtained with the use of algorithmically derivedimage-based features.

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MS8: Theory and Practice of Machine Learning (Part II)

Organizers: Viktor Reshniak, Oak Ridge National Laboratory

Joseph Daws, University of Tennessee Knoxville

Description: The recent explosion of research into artificial intelligence, machine learning, and neuralnetworks across many academic disciplines has led to a gigantic zoo of acronyms andconcepts many of which are variations of some core ideas: modeling, approximation,and optimization. These concepts have been examined extensively by the mathemati-cal and statistical communities. Establishing meaningful connections between mathe-matical and statistical theory to machine learning problems is yielding many positiveresults such as better interpretability of machine learning models, better quantifica-tion of stability and robustness, and improved optimization techniques for trainingneural networks. This minisymposium showcases current research demonstrating newtheoretical and practical understanding of machine learning problems.

Talksdetails:

1. Robust learning with implicit residual networksViktor Reshniak, Oak Ridge National Laboratory

2. Bayesian topological learningCassie Putman Micucci, University of Tennessee Knoxville

Abstract. This presentation explores the computation of posterior distributions froma new Bayesian framework for persistence diagrams. We explain our proposed Bayesianparadigm, which adopts a point process characterization of persistence diagrams. Thisframework provides the flexibility to estimate the posterior cardinality and intensity ofpersistence diagrams simultaneously. We present a closed form of the posterior intensityand cardinality using Gaussian mixtures and binomial distributions. Based on this form,we implement an effective Bayes factor classification algorithm on filament network dataof plant cells. This work is joint with Vasileios Maroulas and Farzana Nasrin.

3. Active learning of tissue-mimicking 3D-printing under censoring, withapplication for surgical planningJialei Chen, Georgia Institute of Technology

Abstract. 3D-printed medical prototypes, which use synthetic metamaterials to mimicbiological tissue, are becoming increasingly important in surgical applications. However,the experiments of mimicking tissue properties via 3D-printed metamaterial may be ham-pered by response censoring, which results in a significant loss of information. For suchcensored experiments, active learning (or experimental design) is paramount for maximiz-ing predictive power using a small number of expensive experimental runs. To tackle this,we propose a novel adaptive design method, called the integrated censored mean-squarederror (ICMSE) method. Our ICMSE method first learns the underlying censoring behav-ior, then adaptively chooses the next points which minimize predictive uncertainty undercensoring. Under a Gaussian process regression model with product Gaussian correlationfunction, the proposed ICMSE criterion has a nice closed-form expression, which allowsfor efficient optimization. We demonstrate the effectiveness of the ICMSE method in theapplication on surgical planning via tissue-mimcking 3D-printing.

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4. High-fidelity computed tomography: from model-based to data-drivenapproachesSinganallur Venkatakrishnan, Oak Ridge National Laboratory

Abstract. Computed Tomography (CT) systems play a vital role in various scientific in-vestigations and non-destructive characterization applications. Central to all CT systemsare algorithms that solve an inverse problem. The first-wave of CT systems typicallyrelied on fast algorithms to invert the measurements based on analytic inversion tech-niques. However, the performance of these algorithms can be poor when dealing withnon-linearities in the measurement, the presence of high-levels of noise, and the limitednumber of measurements that commonly occur when we seek to dramatically acceleratethe imaging.

In this talk, we will present algorithms for improving the performance of CT systems -enabling faster, more accurate and novel tomographic imaging capabilities. The first partof the talk will briefly highlight model-based image reconstruction (MBIR) algorithms forCT based on regularized inversion approaches. We will illustrate how MBIR approacheshave helped to improve system performance for neutron CT, X-ray micro-CT, single par-ticle CryoEM and ultrasound CT systems. The next part of the talk will focus on howto further improve the performance of MBIR algorithms using data-driven/learnt convo-lutional dictionary regularizers with a "plug-and-play" priors approach. Finally, I willhighlight some recent results of using deep-learning techniques for fast CT reconstructionand present challenges that exist in extending the use of such techniques for a genericinstrument.

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MS9: Advances in Theory and Methods for High-dimensional Approxima-tions (Part I)

Organizers: Hoang Tran, Oak Ridge National Laboratory

Armenak Petrosyan, Oak Ridge National Laboratory

Description: The approximations of high-dimensional systems from data play a pivotal role in a widevariety of mathematical and scientific problems including uncertainty quantification,control and optimization, statistical inference and data processing. Such problemsoften require repetitive, expensive measurements (for instance, ensemble of complexnumerical simulations or time-consuming physical experiments), thus, it would be verybeneficial to have access to an accurate surrogate model, which can be used in placeof the original model, to approximate the input-output relationship of interest. Thismini-symposium aims at bringing together people working on the theory and meth-ods for high-dimensional approximation, in particular, but not restricted to, nonlinearapproximation, sparse recovery, low-rank approximation and deep neural networks,showcasing the latest results on both methodology and applications.

Talksdetails:

1. Neural network integral representations and sparse networksArmenak Petrosyan, Oak Ridge National Laboratory Abstract. Machine learningand data analysis techniques have generated a lot of new opportunities in recent years forsolving previously unfeasible complex problems. Although these techniques show amazingperformance in practice, many of their properties are not fully understood, requiring rig-orous mathematical exposition. This presentation will focus on artificial neural networks,which are computationally simple parametric functions with powerful approximation prop-erties. We will use harmonic analysis and optimization tools to develop a theory of neuralnetwork integral representations to elucidate their theoretical features and help addresspractical challenges. In this context, a non-convex regularization method will be proposedto overcome the issues related to network overparametrization.

2. Identification of linear dynamical systems via dataFatih Gelir, University of Texas at Dallas Abstract. We present two algorithms foridentification of unknown discrete time linear systems via several known linear measure-ments, a non-convex optimization problem in general. Nevertheless, our iterations areguaranteed to decrease a certain cost functional associated with this problem. Time per-mitting will show how one of these two algorithms be reformulated as a linear system witha block tridiagonal and nearly block Toeplitz matrix.

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3. Effects of depth, width and initialization: a convergence analysis oflayer-wise training for deep linear networksYeonjong Shin, Brown University

Abstract. In this talk, we will discuss a layer-wise training for deep linear networks.Layer-wise training is an alternative of end-to-end back-propagation, which trains a sin-gle layer at a time, rather than trains the whole layers simultaneously. We consider alayer-wise training by block coordinate gradient descent (BCGD). We establish a generalconvergence analysis of BCGD and found the optimal learning rate. More importantly,the optimal learning rate can directly be applicable in practice. Thus, tuning learning rateis not needed at all. Furthermore, we identify the effects of depth, width and initializationin the training processes. We show that when the identity- like initialization is employed,the width of intermediate layers plays no role in gradient-based training processes, after acertain threshold. We also show that under some conditions, the deeper the network is, thefaster convergence is obtained. This implies that in an extreme case, the global optimumis achieved after updating each weight matrix only once. Even the computational costis considered, we found that a similar conclusion could follow. Numerical examples areprovided to justify our theoretical findings and demonstrate the performance of BCGD.

4. Asymptotic properties of the minimizers of short range scale-invariantinteraction energiesAlex Vlasiuk, Florida State University

Abstract. For a collection of 𝑁 distinct points 𝜔𝑁 in a compact set Ω ⊂ R𝑝, define thetruncated Riesz energy as

𝐸𝑘(𝜔𝑁 ) =

𝑁∑︁𝑖=1

∑︁𝑗∈𝐼𝑖,𝑘

‖𝑥𝑖 − 𝑥𝑗‖−𝑠, 𝑠 > 0,

where 𝐼𝑖,𝑘 denotes the set of indices of the 𝑘 nearest neighbors to the point 𝑥𝑖 in 𝜔𝑁 . Wediscuss the asymptotic properties of the configurations 𝜔*

𝑁 that minimize 𝐸𝑘, and obtainthe asymptotics of the minimal energy and the limiting weak* distribution. We then showhow to augment the above energy functional with a weight and an external field term,allowing to recover a distribution with the given density with respect to the Hausdorffmeasure on Ω.

MS9: Advances in Theory and Methods for High-dimensional Approxima-tions (Part II)

Organizers: Hoang Tran, Oak Ridge National Laboratory

Armenak Petrosyan, Oak Ridge National Laboratory

Description: The approximations of high-dimensional systems from data play a pivotal role in a widevariety of mathematical and scientific problems including uncertainty quantification,control and optimization, statistical inference and data processing. Such problemsoften require repetitive, expensive measurements (for instance, ensemble of complexnumerical simulations or time-consuming physical experiments), thus, it would be verybeneficial to have access to an accurate surrogate model, which can be used in placeof the original model, to approximate the input-output relationship of interest. Thismini-symposium aims at bringing together people working on the theory and meth-ods for high-dimensional approximation, in particular, but not restricted to, nonlinearapproximation, sparse recovery, low-rank approximation and deep neural networks,showcasing the latest results on both methodology and applications.

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Talksdetails:

1. Data-driven tensor decompositionTingran Gao, University of Chicago

Abstract. Viewing tensors as multilinear maps, we propose a novel computationalframework based on interpreting tensor decomposition as empirical risk minimization instatistical learning. Decompositions such as CP, symmetric, orthogonal, and tensor net-work can all be pursued in this unified framework. Our statistical learning methodologyis particularly useful for determining the numerical ranks of structural tensors associatedwith numerical linear algebraic algorithms, some which are of primary interest to com-putational complexity theory.We analyze the optimization landscape of some particularinstances of this tensor decomposition framework, which turns out to have no spuriouslocal minimum.

2. Estimates of entropy numbers in high-dimensional space and applica-tions to compressed sensingHoang Tran, Oak Ridge National Laboratory

Abstract. In this talk, I will discuss some recent strategies for estimation of entropynumber in high-dimensional space. In particular, we show that certain relaxations of(pseudo-)metric can reduce the entropy number and significantly lessen its dependence ondimension. With this improvement, we obtain new conditions on sample complexity forsparse polynomial approximations with l1 regularization.

3. Tensor completion through total variation with initialization fromweighted HOSVDLongxiu Huang, University of California, Los Angeles

Abstract. In our paper, we have studied the tensor completion problem when the sam-pling pattern is deter-ministic. We first propose a simple but efficient weighted HOSVDalgorithm for recovery from noisy observations.Then we use the weighted HOSVD resultas an initialization for the total variation. We have proved the accuracy of the weightedHOSVD algorithm from theoretical and numerical perspectives. In the numerical simu-lation parts,we also showed that by using the proposed initialization,the total variationalgorithm can efficiently fill the missing data for images and videos.

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MS10: Advances in Mathematical Finance and Optimization (Part I)

Organizers: Ekren Ibrahim, Florida State University

Arash Fahim, Florida State University

Description: The goal of this mini-symposium is to gather researchers working in mathematical fi-nance and optimization to share their most recent achievement, exchange ideas, andreceive in-person feedback from their colleagues. This area is one of the vibrant ar-eas in applied mathematics with significant interest in among financial industries andregulators.

Talksdetails:

1. Systemic risk in networks with a central nodeHamed Amini, Georgia State University

2. Multilevel Monte Carlo for LIBOR market modelArun Kumar Polala, Florida State University

Abstract. The multilevel Monte Carlo method is a recently introduced Monte Carloalgorithm. It improves the efficiency of crude Monte Carlo, and as a result, has beenapplied extensively in numerical stochastic differential equations. The LIBOR marketmodel is a popular interest rate model used for pricing interest rate derivatives like caplets,caps, swaptions, etc. In this talk, we will discuss the multilevel Monte Carlo method, andits application to the LIBOR market model. This is joint work with Giray Okten (FloridaState University).

3. Monitoring in principal-agent problemArash Fahim, Florida State University

Abstract. We study a version of the principal-agent problem where the principal canchoose to have access to some hidden information after paying a cost. We provides aclosed-form solution which completely describes the optimal contract, when it is optimalto pay for more information, and the sensitivity of these actions with respect to variousparameters of the problem.

4. Sharing profits in the sharing economyGu Wang, Worcester Polytechnic Institute

Abstract. A monopolist platform (the principal) shares profits with a population of af-filiates (the agents), heterogeneous in skill, by offering them a common nonlinear contractcontingent on individual revenue. The principal cannot discriminate across individualskill, but knows its distribution and aims at maximizing profits. This paper identifiesthe optimal contract, its implied profits, and agents’ effort as the unique solution to anequation depending on skill distribution and agents’ costs of effort. If skill is Pareto-distributed and agents’ costs include linear and power components, closed-form solutionshighlight two regimes: If linear costs are low, the principal’s share of revenues is insensi-tive to skill distribution, and decreases as agents’ costs increase. If linear costs are high,the principal’s share is insensitive to the agents’ costs and increases as inequality in skillincreases.

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MS10: Advances in Mathematical Finance and Optimization (Part II)




Talksdetails:

1. Coupling and characterization of solutions to BSDEsGordan Zitkovic, University of Texas at Austin

Abstract. A new characterization for solutions to backward stochastic differential equa-tions (BSDEs) in dimension 1 is given. It is then used to provide a general stability resultsin the convergence of uniform convergence in probability (ucp). In conjunction with a cou-pling argument, these results provide another proof of the celebrated existence theoremof Kobylanski. This is joint work with Joseph Jackson.

2. A polynomial chaos-based approach to brownian path generationJamie Fox, Florida State University

Abstract. In this talk, we will investigate the use of polynomial chaos in quasi-MonteCarlo simulation. To motivate our approach, we will survey the various Brownian pathgeneration methods in the literature, including those based on Taylor approximations ofthe payoff. Additionally, we will review the concept of effective dimension, and show howthese measurements relate to the effectiveness of quasi-Monte Carlo. We will then intro-duce our orthogonal transformation based on the 2nd order polynomial chaos expansionof the payoff function, and discuss its relationship to the effective dimension. Finally, wewill analyze numerical results for equity options in the Black-Scholes framework as wellas interest rate options in the Libor Market Model.

3. Path-dependent PDEs and optimal control in infinite dimensionsChristian Keller, University of Central Florida

Abstract. Path-dependent PDEs are PDEs defined on path spaces consisting of con-tinuous or cadlag functions. Those PDEs appear naturally in non-Markovian problemsin optimal control, probability, and mathematical finance, for example, optimal control ofdelay equations or pricing of path-dependent options. Moreover, PPDEs have turned outto be essential in the study of certain (even Markovian) problems related to the optimalcontrol of infinite-dimensional evolution equations. In this talk, I will give an overview ofthe theory of viscosity solutions of path-dependent PDEs of first and second order and Iwill address recent developments as well as some open problems.

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4. A general solution technique for insider problems using optimal trans-portFrancois Cocquemas, Florida State University

Abstract. Despite its success, a major limitation of the Kyle (1985) model of informedtrading has been the difficulty to find an equilibrium under anything but restrictive as-sumptions, especially with multiple assets and/or with options. For multiple primaryassets, the state-of-the-art imposes Gaussian price priors and two periods. For options,little has been done since the Back (1993) model, which only considers one stock and oneat-the-money option, a Gaussian price prior, and a very particular noise structure. Theseconstraints limit these models’ applicability.

In this paper, we present a flexible technique to solve a continuous-time multi-asset/multi-option Kyle’s model under general assumptions, including on the (possibly time-varying)distribution of the noise, and the distribution of the prior. The main insight is to pos-tulate the pricing rule of the market maker at maturity as an optimal transport map.The optimal control of the insider reduces to the computation of a conjugate convex func-tion, explicit in some cases, and otherwise easily computed numerically. To illustrate themethod, we solve a problem left open since the seminal contribution of Back (1993): howis option pricing with a non-Gaussian price prior affected by informed traders? In thelognormal case, we compare our results to Black-Scholes, and quantify the price distortionof the option due to strategic trading. We also apply our methodology to the equilibriumwith multiple options.

MS10: Advances in Mathematical Finance and Optimization (Part III)




Talksdetails:

1. Asymptotics for the time-discretized log-normal SABR modelDan Pirjol, Stevens Institute of Technology

Abstract. We propose a novel time discretization for the log-normal SABR model𝑑𝑆𝑡 = 𝜎𝑡𝑆𝑡𝑑𝑊𝑡, 𝑑𝜎𝑡 = 𝜔𝜎𝑡𝑑𝑍𝑡, with 𝑐𝑜𝑟𝑟(𝑊𝑡,𝑍𝑡) = 𝜌, which is a variant of the Euler-Maruyama scheme, and study its asymptotic properties in the limit of a large numberof time steps 𝑛 → ∞ under certain rescaling of the model parameters. We derive analmost sure limit and a large deviations result for the log-asset price in the 𝑛 → ∞limit. The large deviations result is used to derive option price asymptotics and an exactrepresentation for the implied volatility surface in the limit considered.

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2. Quasi-Monte Carlo simulation of copulas for option pricing and VaRestimationYiran Chen, Florida State University

Abstract. Multivariate models with dependent variables are popular in financial indus-try. Simulation of copulas can be done by Monte Carlo methods or quasi-Monte Carlomethods. Goodness-of-fit tests can be used to find the best simulation algorithms for copu-las. We introduce a new goodness-of-fit test based on the collision test and low-discrepancysequences, and present numerical results on option pricing and VaR estimation via copulamodels.

3. Delivering multi-specialty care via online telemedicine platformsLingjiong Zhu, Florida State University

Abstract. The online telemedicine platforms represent a rapidly growing segment ofhealthcare delivery markets. In this paper, we develop a model of telemedicine platformoperations that focuses on managing multi-specialty online-based care in the presenceof general/specialty demand interaction. While such demand interaction is common inpractice, its impact on platform and physician decisions has not received sufficient atten-tion in the operations literature. Our paper focuses on providing guidance on managingmulti-specialty telemedicine platforms. We formulate a queueing model of online servicewith multiple interacting demand and supply types. In our model, the platform sets thepatient fees and physician compensation levels, and physicians, anticipating equilibriumpatient demand response, follow by deciding whether to join the platform, and how muchof their capacity to allocate to the platform. We derive closed-form expressions for theoptimal physician and platform policies in the presence of demand interaction betweenthe general and specialist demand streams. Moreover, we quantify the impact of policiesthat explicitly account for demand interaction on the platform profitability. Our analy-sis describes optimal management policies for multi-specialty telemedicine platforms andprovides a foundation for the study of the role of telemedicine platforms within broaderpatient-centric healthcare ecosystems.

4. Constrained non-concave utility maximization of a variable annuity pol-icyholderAdriana Ocejo Monge, University of North Carolina at Charlotte

Abstract. We discuss a portfolio management problem of the rational policyholder ofa variable annuity (VA) with maturity guarantee who aims to maximize the utility ofher terminal wealth. We consider a VA contract which allows the policyholder to modifyher investment mix throughout the contract. This problem is formulated in terms ofconstrained optimal stochastic control and requires the maximization of a non-concaveutility function. We solve the problem using a martingale approach and compare withexisting results. In particular, we show that there exist different ways to set the guaranteefee, which impacts the policyholder’s optimal investment strategy and the resulting costto the insurer.

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MS11: Reduced Order Models and Data (Part I)

Organizers: Jeff Borggaard, Virginia Tech

Honghu Liu, Virginia Tech

Description: This minisymposium emphasizes reduced order models that are generated using sam-pled data. Applications include control and uncertainty quantification for systemsdescribed by partial differential equations.

Talksdetails:

1. The polynomial-quadratic regulator control problemJeff Borggaard, Virginia Tech

Abstract. Feedback control problems involving autonomous polynomial systems areprevalent, yet there are limited algorithms for approximating their solution. This paperrepresents a step forward in the special case where the state equation has a polynomialnonlinearity, the control costs are quadratic, and the feedback control is approximated bylow-degree polynomials. As it represents the natural extension of the linear-quadratic reg-ulator (LQR) and quadratic-quadratic regulator (QQR) problems, we denote this class aspolynomial-quadratic regulator (PQR) problems. We specifically address problems wherethe state equations are quadratic or cubic, though extensions to higher degree polynomialnonlinearities are presented, and an algorithm based on Al’Brekht’s method is developed.The present approach is amenable to feedback laws with low degree polynomials and mod-est model dimension that could be achieved in many problems by modern model reductionmethods. The Al’Brekht algorithms applied to this class of polynomial nonlinearities hasan elegant formulation using Kronecker products and leads to large linear systems thatcan be effectively solved with an N-way generalization of the Bartels-Stewart algorithm.We demonstrate this algorithm using numerical examples that include the Lorenz equa-tions and discretized versions of Burgers equations and a coupled system of van der Poloscilators. Comparisons to linear feedback control laws show a modest benefit using thenonlinear feedback formulation for these PQR problems.

2. Data-driven variational multiscale reduced order modelsBirgul Koc, Virginia Tech

Abstract. We propose a new data-driven reduced order model (ROM) framework thatcenters around the hierarchical structure of the variational multiscale (VMS)methodologyand utilizes data to increase the ROM accuracy at a modest computational cost. TheVMS methodology is a natural fit for the hierarchical structure of the ROM basis: Inthe first step, we use the ROM projection to separate the scales into three categories: (i)resolved large scales, (ii)resolved small scales, and (iii) unresolved scales. In the secondstep, we explicitly identify the VMS-ROM closure terms, i.e., the terms representing theinteractions among the three types of scales. In the third step, we use available datato model the VMS-ROM closure terms. Thus, instead of phenomenological models usedin VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilizeavailable data to construct new structural VMS-ROM closure models. Specifically, webuild ROM operators(vectors, matrices, and tensors) that are closest to the true ROMclosure terms evaluated with the available data.

3. Reduced order models for variable density flow and transport equationsOlcay Cifti, Auburn University

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4. Data-driven closure strategies for reduced order models of the quasigeostrophicChanghong Mou, Virginia Tech

Abstract. We will present a recently introduced data-driven correction reduced ordermodel (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. TheDDC-ROM uses available data to model the correction term that is generally used torepresent the missing information in low-dimensional ROMs. Physical constraints areadded to the DDC-ROM to create the constrained data-driven correction reduced ordermodel (CDDC-ROM) in order to further improve its accuracy and stability. Finally, theDDC-ROM is tested on time intervals that are longer than the time interval over which itwas trained. The numerical investigation shows that, for low-dimensional ROMs, both theDDC-ROM and CDDC-ROM perform better than the standard Galerkin ROM (G-ROM)and the CDDC-ROM provides the best results.

MS11: Reduced Order Models and Data (Part II)

Organizers: Jeff Borggaard, Virginia Tech

Honghu Liu, Virginia Tech

Description: This minisymposium emphasizes reduced order models that are generated using sam-pled data. Applications include control and uncertainty quantification for systemsdescribed by partial differential equations.

Talksdetails:

1. Quasi-optimal sparse grids method for periodic functionsMiroslav Stoyanov, Oak Ridge National Laboratory

Abstract. We consider adaptive sparse grid interpolation applied to periodic functionsof finite differentiability, with application to molecular potential energy surfaces models.Approximation uses a basis of trigonometric polynomials with coefficients computed bymultidimensional fast-Fourier-transform. The adaptive procedure infers the decay of theFourier coefficients using an anisotropic quasi-optimal estimate for the best approxima-tion space. The procedure is implemented in the Tasmanian UQ library, adaptivity isperformed using distributed (MPI) asynchronous sampling algorithm.

2. Efficient sampling methods for uncertainty quantification over variableresolution parameter spacesHans-Werner van Wyk, Auburn University

Abstract. The viability of efficient interpolatory sampling methods, used to approxi-mate statistical quantities of interest related to uncertain physical systems, is limited bythe complexity of the underlying parameter space. Monte Carlo sampling methods on theother hand, while less efficient, have an accuracy that depends only on the sampled quan-tity’s variance. In this talk, we combine these two sampling methods in a complementaryway, by splitting the parameter space into a low-complexity/high-variance component thatcan be resolved by means of interpolatory surrogates, and a high-complexity/low-variancepart for which Monte Carlo sampling is well-suited. We show how this hybrid methodreduces the overall computational cost and demonstrate its features with the help of afew computational experiments.

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3. A sparse-grid probabilistic scheme for approximation of the runwayprobability of electrons in fusion tokamak simulationMinglei Yang, Oak Ridge National Laboratory

Abstract. Runaway electrons (RE) generated during magnetic disruptions present amajor threat to the safe operation of fusion tokamas. A critical aspect of understandingRE dynamics is to calculate runaway probabilities, i.e., the probability of an electron inthe phase space will runaway on, or before, a time 𝑡 > 0. In the talk, I will presenta sparse-grid probabilistic scheme for computing runaway probability. The sparse gridinterpolation is utilized to approximate the runaway probability, and adaptive refinementis also exploited to handle the sharp transition layer between the runaway and non-runaway region. Two numerical examples are shown to demonstrate the performance ofthe proposed approach.

MS12: Theory and Numerics for Resonances and Related Spectral Problemsin Optics and Electromagnetics (Part I)

Organizer: Junshan Lin, Auburn University

Description: Resonances and related eigenvalues can give rise to various interesting phenomena inoptics and electromagnetics, which leads significant applications in physics and engi-neering. Their mathematical studies also received increasing attention in recent years.This mini-symposium seeks to bring together researchers to promote exchange of ideas,and present recent theoretical and computational developments for resonances andother emerging eigenvalues problems in optics and electromagnetics, and their applica-tions. Some recent aspects of interest are plasmonic resonances, spectrally embeddedbound states, topologically protected states, transmission eigenvalues, etc.

Talksdetails:

1. Aspects of the spectrum of multi-layer graphene-type graph operatorsStephen Shipman, Louisiana State University

Abstract. For a graph model of several stacked layers of graphene, the dispersionfunction of wave vector and energy is shown to be a polynomial in the dispersion functionof the single layer. This leads to the reducibility of the Fermi surface, at any energy,into several components. Each component corresponds to hybrid states in the multi-layerstructure that contribute a sequence of bands to the spectrum. Both AA- and AB-stackingare allowed. The reducibility allows the creation of local defects that engender embeddedeigenvalues. Distributing defects at a mesoscale and homogenizing leads to materials withnarrow "embedded spectral bands". This construction can be generalized to a class ofperiodic graph operators.

2. Finite element approximation of nonlinear eigenvalue problemsJiguang Sun, Michigan Technological University

Abstract. Nonlinear eigenvalue problems of partial differential equations have manyimportant applications in science and engineering. In this talk, we present a new finiteelement approach based on the spectral theory of holomorphic Fredholm operator func-tions and the associated abstract approximation. Since the eigenvalues are complex ingeneral, we propose a new method, called the spectral indicator method, to compute allthe eigenvalues in a region on the complex plane. The new theory is applied to studytwo nonlinear eigenvalue problems arising from the design of subwavelength metallic slitstructures and the inverse scattering theory for anisotropic media

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3. Controlling refraction using sub-wavelength resonatorsYue Chen, Auburn University at Montgomery

Abstract. We construct metamaterials from sub-wavelength nonmagnetic resonatorsand consider the refraction of incoming signals traveling from free space into the meta-material. We show that the direction of the transmitted signal is a function of its centerfrequency and bandwidth.The directionality of the transmitted signal and its frequencydependence is shown to be explicitly controlled by sub-wavelength resonances that can becalculated from the geometry of the sub-wavelength scatters. We outline how to constructa medium with both positive and negative index properties across different frequencybands in the near infrared and optical regime.

4. Electron dynamics in novel materials: waves at degeneracies and edgesAlexander Watson, Duke University

Abstract. The wave-like dynamics of electrons in materials are governed by PDESchrodinger equations. These dynamics give rise to the materials’ electronic properties,for example: whether the material is a conductor or an insulator. I will discuss electrondynamics in two classes of materials which have attracted considerable attention in recentyears for applications: Dirac semi-metals (e.g. graphene), and topological insulators. Iwill explain how the exciting properties of these materials create interesting mathemati-cal challenges for both rigorous analysis and numerical computation. I will then presentmy own work, which focuses on overcoming these difficulties. I will then discuss futuredirections of this work.

MS12: Theory and Numerics for Resonances and Related Spectral Problemsin Optics and Electromagnetics (Part II)

Organizer: Junshan Lin, Auburn University

Description: Resonances and related eigenvalues can give rise to various interesting phenomena inoptics and electromagnetics, which leads significant applications in physics and engi-neering. Their mathematical studies also received increasing attention in recent years.This mini-symposium seeks to bring together researchers to promote exchange of ideas,and present recent theoretical and computational developments for resonances andother emerging eigenvalues problems in optics and electromagnetics, and their applica-tions. Some recent aspects of interest are plasmonic resonances, spectrally embeddedbound states, topologically protected states, transmission eigenvalues, etc.

Talksdetails:

1. Convergence of an HDG finite element method for Maxwell’s equationsin an inhomogeneous mediumPeter Monk, University of Delaware

Abstract. We propose to use a hybridizable discontinuous Galerkin (HDG) methodcombined with the continuous Galerkin (CG) method to approximate Maxwell’s equa-tions. We derive optimal convergence estimates for our HGD-CG approximation whenthe electromagnetic coefficients are piecewise smooth. This requires new techniques ofanalysis adapting the work of Buffa and Perugia to HDG. Second, we use CG elementsto approximate the Lagrange multiplier used to enforce the divergence condition and weobtain a discrete system in which we can decouple the discrete the Lagrange multiplier.Because we are using a continuous Lagrange multiplier space, the number of degrees offreedom devoted to this are less than for other HDG methods. We present numericalexperiments to confirm our theoretical results.

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2. Backward waves in corrugated wave guides with dispersion controlledby plasmonic resonancesRobert Lipton, Louisiana State University

Abstract. Motivated by the numerical experiments carried out in [S. C. Yurt, A. El-frgani, M. I. Fuks, K. Ilyenko, and E. Schamiloglu, IEEE Trans. Plasma Sci., 44 (2016),pp. 1280–1286], we apply an asymptotic analysis to show that corrugated waveguidescan be approximated by smooth cylindrical waveguides with an effective metamaterialsurface impedance. We show that this approximation is in force when the period of thecorrugations is subwavelength. Here the metamaterial delivers an effective anisotropicsurface impedance and imparts novel dispersive effects on signals traveling inside thewaveguide. These properties arise from the subwavelength resonances inside the corru-gations. For suciently deep corrugations, the metamaterial waveguide predicts backwardwave propagation. In this way we may understand backward wave propagation as a mul-tiscale phenomenon resulting from local resonances inside subwavelength geometry. Ourapproach is well suited to numerical computation, and we provide a systematic investiga-tion of the effect of corrugation geometry on wave dispersion, group velocity, and powerflow.

3. A high-Order perturbation of envelopes (HOPE) method for scatteringby periodic inhomogeneous mediaDavid Nicholls, University of Illinois at Chicago

Abstract. The interaction of linear waves with periodic structures arises in a broadrange of scientific and engineering applications. For such problems it is often mandatorythat numerical simulations be rapid, robust, and highly accurate. With such qualities inmind High-Order Spectral methods are often utilized, and in this talk we describe and testa perturbative method which fits into this class. Here we view the inhomogeneous (butlaterally periodic) permittivity as a perturbation of a constant value and pursue (regular)perturbation theory. We demonstrate that not only does this lead to a fast and accuratenumerical method, but also that the expansion of the field in this geometric parameter isvalid for large deformations (up to topological obstruction). Finally, we show that, if thepermittivity deformation is spatially analytic, then so is the field scattered by it.

4. Optical phenomena and resonances in the homogenization of layeredheterostructuresMatthias Maier, Texas A&M University

Abstract. In this talk we present analytical and computational approaches to simulateresonant effects of surface plasmon polaritons (SPPs) on 2D material interfaces and lay-ered heterostructures. The computational approach is based on a homogenization theoryfor layered heterostructures and an adaptive finite-element simulation framework. Wediscuss how the cell problem gives rise to surface plasmon resonances (SPRs) and howthe resonances contribute to the Lorentz resonance observed in the effective permittivityof the homogenized material. We present some preliminary computational results thatindicate that the homogenization error is well controlled even for finite-sized systems offew layers.

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MS13: Recent Development of Coupled Problems with Advanced PhysicsBased Numerical Methods (Part I)

Organizer: Sanghyun Lee, Florida State University

Description: This minisymposium seeks to gather the most recent advancements in numericalmethods for any applications including fluid dynamics, subsurface modeling, frac-ture mechanics, and more. The high fidelity simulation of these realistic phenom-ena involves highly heterogeneous media, multiple spatial and temporal scales, andlarge domains. Even under basic modeling assumptions, these systems are compu-tationally intensive and require specialized techniques for efficient solution while pre-serving accuracy. In particular, this session will include topics on any finite differ-ence/element/volume methods, adaptive mesh refinement, specialized discretizations,and data driven computations.

Talksdetails:

1. Enriched Galerkin for coupled flow and transportSanghyun Lee, Florida State University

Abstract. We present and analyze enriched Galerkin finite element methods (EG) tosolve a coupled system in porous media such as flow, transport, and the Biot system.The EG is formulated by enriching the conforming continuous Galerkin finite elementmethod (CG) with piecewise constant functions. This approach is shown to be locallyand globally conservative while keeping fewer degrees of freedom in comparison withdiscontinuous Galerkin finite element methods (DG). Linear solvers and dynamic meshadaptivity techniques using entropy residual and hanging nodes will be discussed. Somenumerical tests in two and three dimensions are presented to confirm our theoreticalresults as well as to demonstrate the advantages of the EG.

2. Weak Galerkin finite element methods for Brinkman equationsLin Mu, University of Georgia

Abstract. In this talk, we shall introduce a robust weak Galerkin finite element schemefor Brinkman equations. The major idea for achieving the uniform energy-error estimateis to use a divergence preserving velocity reconstruction operator in the discretization.The optimal convergence results for velocity and pressure have been established. Thistechnique will be first introduced for solving the Stokes equations and then extendedto Brinkman equations. Finally, numerical examples are presented for validating thetheoretical conclusions.

3. Adaptive mesh refinement for Cut Finite Element MethodCuiyu He, University of Georgia

Abstract. In this talk, we introduce, analyze and implement a residual based a pos-teriori error estimation for the CutFEM fictitious domain method applied to an ellipticmodel problem. We consider the problem with smooth (non-polygonal) boundary and,therefore, the analysis takes into account both the geometry approximation error on theboundary and the numerical approximation error. Theoretically we can prove that theerror estimation is both reliable and efficient. Moreover, the error estimation is robust inthe sense that both the reliability and efficiency constants are independent of the arbitraryboundary-mesh intersection.

4. Simulation of precipitation reactions in dicrofluidic devicesPatrick Eastham, Florida State University

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MS13: Recent Development of Coupled Problems with Advanced PhysicsBased Numerical Methods (Part II)

Organizer: Sanghyun Lee, Florida State University

Description: This minisymposium seeks to gather the most recent advancements in numericalmethods for any applications including fluid dynamics, subsurface modeling, frac-ture mechanics, and more. The high fidelity simulation of these realistic phenom-ena involves highly heterogeneous media, multiple spatial and temporal scales, andlarge domains. Even under basic modeling assumptions, these systems are compu-tationally intensive and require specialized techniques for efficient solution while pre-serving accuracy. In particular, this session will include topics on any finite differ-ence/element/volume methods, adaptive mesh refinement, specialized discretizations,and data driven computations.

Talksdetails:

1. High order FFT Poisson solvers for interface and boundary value prob-lemsShan Zhao, University of Alabama

Abstract. In this talk, we will introduce an augmented matched interface and bound-ary (AMIB) method for solving elliptic interface and boundary value problems. For anarbitrarily curved interface in 2D, the AMIB method can restore the order of the centraldifference scheme to two, by rigorously enforcing the jump conditions. Moreover, by em-ploying a Schur complement procedure, the discrete Laplacian of the central differencecan be efficiently inverted by using the fast Fourier transform (FFT), so that the overallcomputational efficiency of the FFT-AMIB is about 𝑂(𝑁2𝑙𝑜𝑔𝑁) for a 𝑁2 grid in 2D. Ingeneralizing the AMIB method to even higher order, we also considered elliptic boundaryvalue problems over cubic domains. For such problems, the AMIB method provides thefirst FFT Poisson solver in the literature that is constructed based on high order centraldifference schemes. As a systematic approach, the AMIB method can be made to arbitrar-ily high order in principle. Up to 8th order is demonstrated numerically. Moreover, theAMIB method can handle Dirichlet, Neumann, and Robin boundary conditions, and theirmix combinations. The FFT-AMIB method can be easily applied in multi-dimensions,with a complexity of 𝑂(𝑁3𝑙𝑜𝑔𝑁) for a 𝑁3 grid in 3D.

2. Multirate exponential methods for additively partitioned systems of dif-ferential equationsVu Thai Luan, Mississippi State University

Abstract. For additively partitioned systems, multirate integrators have shown to bemore efficient than traditional time integrators which use a single time step during theintegration process. The idea of these integrators is to employ different time steps forintegrating different components (e.g. fast and slow) of the systems, thereby enhancingcomputational efficiency while ensuring the overall stability and accuracy. In this talk,based on backward error analysis of exponential Runge-Kutta methods, we are able toderive a set of modified fast initial-value problems that must be solved to proceed be-tween slow stages, and thus derive a new family of multirate schemes, called multirateexponential Runge-Kutta (MERK) methods, with orders up to 5 in a much simpler andelegant way compared to previous approaches. A rigorous convergence analysis of MERKmethods was also carried out. Numerical experiments on a set of multirate test problemsare given to confirm the accuracy and efficiency of MERK methods.

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3. Modelling the Navier-Stokes-Darcy-Heat systemMatt McCurdy, Florida State University

Abstract. To investigate convection in coupled fluid-porous media systems, we analyzethe Navier-Stokes-Darcy-Heat model with numerical simulations conducted via a finiteelement method. To help validate numerical results, we determine stability thresholds forthe system with a novel nonlinear stability argument.

Additionally, we investigate various parameter regimes of the system and present a notablecase with altering the depth ratio of the two regions. In these superposed fluid-porous me-dia systems, the ratio of the fluid height to the porous medium height exerts a significantinfluence on the behavior of the coupled system with its impact on resulting convectioncells. Altering the depth ratio slightly can trigger a transition from full-convection whereconvection cells encapsulate the entire domain to fluid-dominated convection where cellsoccupy only the fluid region. With current interest surrounding superposed fluid-porousmedium systems in numerous projects of industrial, environmental, and geophysical im-portance (oil recovery, carbon dioxide sequestration, contamination in sub-soil reservoirs,etc.), being able to predict the critical depth ratio where this convection shift occurs isparticularly timely.

4. New central and central DG-type methods on overlapping cells for Solv-ing MHD Equations on triangular MeshesYingjie Liu, Georgia Tech

Abstract. This talk is based on a recently published paper joint with Zhiliang Xu (U.of Notre Dame). They develop new central and central DG-type methods on overlappingcells for solving nonlinear MHD equations on triangular meshes. This method is fullyconservative for the magnetic field. New features are introduced to reduce the complex-ity: the fluid quantities are only computed on the triangular mesh while the magneticfield is also defined on the dual mesh. These methods take advantage of the nice featureof central schemes to avoid dealing with Riemann problems at discontinuities of the elec-tromagnetic field. They can also take arbitrarily small time step sizes when necessarywithout introducing the 𝑂(1/𝑑𝑡) dissipation error.

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MS14: Some Numerical Algorithms in Scientific Machine Learning

Organizers: Hongchao Zhang, Louisiana State University

Xiaoliang Wan, Louisiana State University

Description: Different type of algorithms arising from different backgrounds and research fields inscientific computing and applied mathematics will be presented in this mini-symposium.These algorithms may have interesting applications in scientific machine learning.

Talksdetails:

1. Deep density estimation via invertible block-triangular mappingXiaoliang Wan, Louisiana State University

Abstract. In this work, we develop an invertible transport map, called KRnet, fordensity estimation by coupling the Knothe-Rosenblatt (KR) rearrangement and the flow-based generative model, which generalizes the real-NVP model. The triangular structureof the KR rearrangement breaks the symmetry of the real NVP in terms of the exchange ofinformation between dimensions, which not only accelerates the training process but alsoimproves the accuracy significantly. We have also introduced several new layers into thegenerative model to improve both robustness and effectiveness, including a reformulatedaffine coupling layer, a rotation layer and a componentwise nonlinear invertible layer. TheKRnet can be used for both density estimation and sample generation especially whenthe dimensionality is relatively high.

2. A self-consistent-field iteration for orthogonal canonical correlationanalysisLi Wang, University of Texas at Arlington

Abstract. We propose an efficient algorithm for solving orthogonal canonical correlationanalysis (OCCA) in the form of trace-fractional structure and orthogonal linear projec-tions. Even though orthogonality has been widely used and proved to be a useful criterionfor pattern recognition and feature extraction, existing methods for solving OCCA prob-lem are either numerical unstable by relying on a deflation scheme, or less efficient bydirectly using generic optimization methods. In this paper, we propose an alternating nu-merical scheme whose core is the sub-maximization problem in the trace-fractional formwith an orthogonal constraint. A customized self-consistent-field (SCF) iteration for thissub-maximization problem is devised. It is proved that the SCF iteration is globallyconvergent to a KKT point and that the alternating numerical scheme always converges.We further formulate a new trace-fractional maximization problem for orthogonal multi-set CCA (OMCCA) and then propose an efficient algorithm with an either Jacobi-styleor Gauss-Seidel-style updating scheme based on the same SCF iteration. Extensive ex-periments are conducted to evaluate the proposed algorithms against existing methodsincluding two real world applications: multi-label classification and multi-view featureextraction. Experimental results show that our methods not only perform competitivelyto or better than baselines but also are more efficient.

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3. Extending the added-mass partitioned (AMP) scheme for solving FSIproblems coupling incompressible flows with elastic beams to 3DLongfei Li, University of Louisiana at Lafayette

Abstract. A new partitioned algorithm was recently developed for solving fluid-structure interaction (FSI) problems coupling incompressible flows with elastic beamsundergoing finite deformations in 2D. The new algorithm, referred to as the Added-MassPartitioned (AMP) scheme, overcomes the added-mass instability that has for decadesplagued partitioned FSI simulations of incompressible flows coupled to light structures.The AMP scheme achieves fully second-order accuracy and remains stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong.The stability and accuracy of the AMP scheme is validated through mode analysis andnumerical experiments. In this talk, we will describe the ongoing progress and challengeon extending the AMP scheme to the 3D regime.

4. A derivative-free geometric algorithm for optimization on a sphereHongchao Zhang, Louisiana State University

Abstract. In this talk, we present a Derivative-Free Geometric Algorithm (DFGA)which takes trust region framework and explores the spherical geometry to solve theoptimization problem with a spherical constraint. Under mild assumptions, we showthat there at least exists a subsequence of the iterates generated by DFGA convergingto a stationary point of this spherical optimization. Furthermore, under the Lojasiewiczproperty, we show that all the iterates generated by DFGA will converge with at leasta linear or sublinear convergence rate. Our numerical experiments show DFGA is veryrobust, efficient and might be very useful for solving practical optimization problems ona sphere without using derivatives.

MS15: Stochastic Optimal Control and Its Applications

Organizers: Feng Bao, Florida State University

Jiongmin Yong, University of Central Florida

Description: Stochastic optimal control is an important topic in mathematics and it has extensiveapplications in biology, chemistry, mathematical finance and various engineering dis-ciplines. In this mini-symposium, we present both theoretical and practical researchoutcomes in stochastic optimal control and explore recent advances in applications ofcontrol theory.

Talksdetails:

1. Linear-Quadratic Optimal Control with Random CoefficientsJiongmin Yong, University of Central Florida

Abstract. This talk is concerned with a stochastic linear-quadratic optimal controlproblem in a finite time horizon, where the coefficients of the control system are allowedto be random, and the weighting matrices in the cost functional are allowed to be randomand indefinite. It is shown, with a Hilbert space approach, that for the existence ofan open-loop optimal control, the convexity of the cost functional (with respect to thecontrol) is necessary; and the uniform convexity, which is slightly stronger, turns out tobe sufficient, which also leads to the unique solvability of the associated stochastic Riccatiequation. Further, it is shown that the open-loop optimal control admits a closed-looprepresentation.

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2. On the asymptotic optimality of the comb strategy for prediction withexpert adviceIbrahim Ekren, Florida State University

Abstract. For the problem of prediction with expert advice in the adversarial settingwith geometric stopping, we compute the exact leading order expansion for the long timebehavior of the value function using techniques from stochastic analysis and PDEs. Then,we use this expansion to prove that as conjectured in Gravin, Peres and Sivan the combstrategies are indeed asymptotically optimal for the adversary in the case of 4 experts.The presentation is based on a joint work with E. Bayraktar, X. Zhang, and Y. Zhang.

3. A Global Maximum Principle for Stochastic Optimal Control Problemswith DelayJingtao Shi, Shandong University

Abstract. In this talk, we solve an open problem for the stochastic optimal control prob-lem with delay where the control domain is non-convex and the diffusion term containsboth the control variable and its delayed term. Inspired by previous results by Oksendaland Sulem in 2000 and Chen and Wu in 2010, we generalize the Peng’s general stochasticmaximum principle in 1990 to the time delayed case, which we called the global maximumprinciple. A new adjoint equation is introduced to deal with the cross terms, when apply-ing the duality technique, though assumption imposed on it is a little strong. Comparingwith the classical result, the maximum condition contains an indicator function, in factit is the characteristic of the stochastic optimal control problem with delay. A solvablelinear-quadratic example is also discussed. (Joint work with Dr. Weijun Meng)

4. Stochastic optimal impulse control with decision lagsChang Li, University of Central Florida

Abstract. In this talk, we consider an impulse control problem in finite horizon withdecision lags. The continuity of the value function is proved. We show that the valuefunction satisfies a suitable version of dynamic programming principle, which takes intoaccount the dependence of state process through the waiting time. The correspondingHamilton-Jacobi-Bellman equations are derived, and exhibit some peculiarities on theform of the differential operators and their domains. We prove a unique characterizationof the value function to this nonstandard PDE system by means of viscosity solutions. Averification theorem with an optimal strategy to our problem is provided. Moreover, alimiting case with the decision lag approaching 0 is discussed.

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MS16: Novel Techniques in Optimization and Applications

Organizer: Guohui Song, Old Dominion University

Description: Optimization models are dominant in many fields including machine learning, signalprocessing, and operation/scheduling problems. When the data size is getting large,traditional optimization algorithms might not be efficient enough to find the optimalsolutions. It would be necessary to study some novel optimization techniques for largesize models including the analysis and applications of such techniques.

Talksdetails:

1. Optimization in infinite-dimensional spacesGuohui Song, Old Dominion University

Abstract. Many models in machine learning and image/signal processing are formu-lated as optimization problems in high(infinite)-dimensional spaces. The large number ofdimension brings a great challenge in computation. Most numerical algorithms would havean enormous (exponential) increase on the complexity when adding extra dimensions, aphenomenon called curse of dimensionality. We would discuss how to move certain op-timization models in a high(infinite)-dimensional space to a smaller subspace withoutsacrificing the accuracy too much (or even at all).

2. Logic-based Benders decomposition for gantry crane scheduling withtransferring position constraints in a rail-road container terminalYi Wang, Auburn University at Montgomery

Abstract. This paper considers the gantry crane scheduling problem in a rail-road con-tainer terminal. Two models using mixed integer programming and constraint program-ming (CP) are developed. A logic-based Benders decomposition (LBBD) methodologyis also proposed. This method exploits a decomposition of the studied problem into arelaxed master problem solved by mixed integer programming (MIP), and a series of sub-problems, solved separately by MIP and CP. The computational results show that the CPapproach is better suited to solve the proposed problem with small-sized and medium-sized instances compared with MIP and LBBD. In addition, the LBBD framework is farsuperior to mixed integer programming on all but a few small instances, and it is highlyeffective in finding good-quality solutions for larger cases with up to 100 tasks. More-over, the results find that LBBD using constraint programming to solve the sub-problemsoutperforms LBBD with mixed integer programming on the instances tested.

3. Polynomial filters of graph shifts and their inverses: theory and localimplementationNazar Emirov, University of Central Florida

Abstract. Polynomial graph filters and their inverses play important roles in graph sig-nal processing. An advantage of polynomial graph filters is that they can be implementedin a distributed manner, which involves data transmission between adjacent vertices only.The challenge arisen in the inverse filtering is that a direct implementation may sufferfrom high computational burden, as the inverse graph filter usually has full bandwidtheven if the original filter has small bandwidth. We consider distributed implementationof the inverse filtering procedure for a polynomial graph filter of multiple shifts, and wepropose two iterative approximation algorithms that can be implemented in a distributednetwork, where each vertex is equipped with systems for limited data storage, compu-tation power and data exchanging facility to its adjacent vertices. We also demonstratethe effectiveness of the proposed iterative approximation algorithms to implement the in-verse filtering procedure and their satisfactory performance to denoise time-varying graphsignals and a data set of US hourly temperature at 218 locations.

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MS17: Theory and Computation for Stochastic Models

Organizers: Xu Wang, Purdue University

Feng Bao, Florida State University

Description: In recent years, increasing attention is drawn to mathematical models that describestochastic phenomenon in both science and engineering disciplines. Theoretical anal-ysis and numerical computation are two important topics that generate challenges tomathematicians who are interested in applying stochastic models to solve practicalproblems The aim of this mini-symposium is to showcase research outcomes from boththeoretical and computational communities regarding stochastic problems.

Talksdetails:

1. Structure-preserving numerical method for stochastic nonlinearSchrodinger equationJianbo Cui, Georgia Institute of Technology

Abstract. It’s know that when discretizing stochastic ordinary equation with non-globally Lipschitz coefficient, the traditional numerical method, like Euler method, maybe divergent and not converge in strong or weak sense. For stochastic partial differentequation with non-globally Lipschitz coefficient, there exists fewer result on the strongand weak convergence results of numerical methods. In this talk, we will discuss severalnumerical schemes approximating stochastic Schrodinger Equation. Under certain con-dition, we show that the exponential integrability preserving schemes are strongly andweakly convergent with positive orders

2. Analytic continuation of noisy data using Adams Bashforth ResNetXuping Xie, Courant Institue, NYU

Abstract. We propose a data-driven learning framework for the analytic continuationproblem in numerical quantum many-body physics. Designing an accurate and efficientframework for the analytic continuation of imaginary time using computational data is agrand challenge that has hindered meaningful links with experimental data. The standardMaximum Entropy (MaxEnt)-based method is limited by the quality of the computationaldata and the availability of prior information. Also, the MaxEnt is not able to solvethe inversion problem under high level of noise in the data. Here we introduce a novellearning model for the analytic continuation problem using a Adams-Bashforth residualneural network (AB-ResNet). The advantage of this deep learning network is that itis model independent and, therefore, does not require prior information concerning thequantity of interest given by the spectral function. More importantly, the ResNet-basedmodel achieves higher accuracy than MaxEnt for data with higher level of noise. Finally,numerical examples show that the developed AB-ResNet is able to recover the spectralfunction with accuracy comparable to MaxEnt where the noise level is relatively small.

3. A splitting up scheme for backward doubly stochastic differential equa-tionsHe Zhang, Auburn University

Abstract. We design a computationally efficient scheme for backward doubly stochasticdifferential equations, using splitting-up techniques. Convergence results are provided.This is a joint work with Feng Bao and Yanzhao Cao.

4. Inverse random source scattering for the Helmholtz equation with at-tenuationXu Wang, Purdue University

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MS18: Recent Development of Finite Element Methods and Related Appli-cations

Organizers: Cuiyu He, University of Georgia

Lin Mu, University of Georgia

Description: This minisymposium will gather the recent development of finite element methods in-cluding CutFEM, Discontinuous Galerkin, weak Galerkin methods and investigate therelated applications. The efficient, accurate, and robust schemes will be discussed.This session will cover applications in geometry optimization, fluid dynamics, mechan-ics, and financing math.

Talksdetails:

1. Cut finite element method for ill-posed Bernoulli free boundary problemCuiyu He, University of Georgia

Abstract. In this talk, we discuss a level set approach for the identification of an un-known boundary in a computational domain. The problem takes the form of a Bernoulliproblem where only the Dirichlet datum is known on the boundary that is to be identified,but additional information on the Neumann condition is available on the known part of theboundary. The approach uses a classical constrained optimization problem, where a costfunctional is minimized with respect to the unknown boundary, the position of which isdefined implicitly by a level set function. To solve the optimization problem a steepest de-scent algorithm using shape derivatives is applied. In each iteration the cut finite elementmethod is used to obtain high accuracy approximations of the pde-model constraint for agiven level set configuration without remeshing. We consider three different shape deriva-tives. First the classical one, derived using the continuous optimization problem (optimizethen discretize). Then the functional is first discretized using the cutFEM method andthe shape derivative is evaluated on the finite element functional (discretize the optimize).Finally we consider a third approached also using a discretized functional. In this case wedo not perturb the domain, but consider a so-called boundary value correction method,where a small correction to the boundary position may be included in the weak boundarycondition. Using this correction the shape derivative may be obtained by perturbing adistance parameter in the discrete variational formulation. The theoretical discussion isillustrated with a series of numerical examples showing that all three approaches producesimilar result on the proposed Bernoulli problem.

2. Adaptive weak Galerkin method for convection-diffusion problemsNatasha Sharma, University of Texas at El Paso

Abstract. The accuracy of numerical solutions to convection-diffusion problems is oftenmarred by the presence of layers in a convection dominated regime. A natural tool toovercome this difficulty is to adaptively refine the mesh in regions where these layers getformed. Based on a weak gradient operator and a weak divergence operator, we presentan adaptive weak Galerkin finite element method which serves this purpose. Results ofnumerical experiments are presented to illustrate the performance of the estimator in thepresence of boundary and interior layers.

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3. A stabilizer free weak Galerkin FEM for general second order ellipticproblemsAhmed Al-Taweel, University of Arkansas at Little Rock

Abstract. This paper proposes a stabilizer free weak Galerkin (SFWG) finite elementmethod for the convection-diffusion-reaction equation in the diffusion-dominated regime.The object of using the SFWG method is to obtain a simple formulation which makesthe SFWG algorithm more efficient and the numerical programming easier. The optimalrates of convergence of numerical errors of 𝑂(ℎ𝑘) in 𝐻1 and 𝑂(ℎ𝑘+1) in 𝐿2 norms areachieved under conditions

(︀𝑃𝑘(𝐾), 𝑃𝑘(𝑒), [𝑃𝑗(𝐾)]2

)︀, 𝑗 = 𝑘 + 1, 𝑘 = 1, 2 finite element

spaces. Numerical experiments are reported to verify the accuracy and efficiency of theSFWG method.

4. Pricing S&P 500 index option with Lévy JumpsBin Xie, University of Georgia

Abstract. We use the method of Bakshi, Chen and Chao (1997) to consistently analyzethe Heston model, non-iid jump model and Lévy jump model for the S&P 500 indexoption. By empirical studies, the Lévy jump for the S&P 500 index is inevitable. Weestimate parameters from in-sample pricing through sum of squared pricing error (SSE)for BS, SV, SVJ, non-iid and Lévy (GH, NIG, CGMY) models, and utilize them for out-of-sample pricing and comparisons among these models. The properties of the sensitivitiesfor Lévy model with respect to parameters are presented due to the FFT approximation.Empirically, we show that the NIG model, SV and SVJ models with estimated volatilityoutperform the other models for both in-sample and out-of-sample periods. Using thein-sample optimized parameters, we find that the NIG model has the least SSE andoutperforms the rest models on one-day prediction.

MS19: Young Researchers in Mathematical Biology

Organizers: Christopher Botelho, University of Central Florida

Poroshat Yazdanbakhshghahyazi, University of Central Florida

Description: Talks will highlight research done by graduate students and young researchers. Thetalks given will provide a diversified perspective of the field of mathematical biology.Applications of nonlinear systems, including ecological models as well as epidemiolog-ical models, will be presented.

Talksdetails:

1. A tale of two microbes: an analysis of vibrio-phage interactionChristopher Botelho, University of Central Florida

Abstract. A mathematical model of V. cholerae incorporating bacterial, phage andhuman populations is developed. Local stability and global stability results of threepotential equilibrium points are discussed. Disease control strategies are discussed withan emphasis on disease control by phage.

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2. Applications of target reproduction numbers in infectious disease mod-elsPoroshat Yazdanbakhshghahyazi, University of Central Florida

Abstract. The problem of eradicating infectious diseases has attracted both mathemati-cians’ and biologists’ attention. This talk focuses mainly on control strategies targetingcertain interactions between and/or within categories of individuals to treat an infectionafter being introduced into a susceptible population. To do so, we develop a new thresholdparameter called the "target reproduction number" and study its application in infectiousdisease models including airborne, waterborne, and direct transmission diseases. We showthat the target reproduction number enables us to target not just certain entries but alsocertain parameters in the next generation matrix. We also analyze different next gen-eration matrices corresponding to the same linearized system, and make the connectionbetween the target reproduction of each.

3. Modeling Disease Immunity Dynamics: Application to Cholera ModelsHenry Chang, University of Miami

Abstract. Immunity against certain infectious diseases may wane over time, resultingin the reemergence of epidemics. Here, I propose a general model to capture the dynam-ics of waning immunity and reinfection on a simple direct transmission disease model.The conditions for disease outbreak and disease-free periods are discussed, along withapplications for cholera disease models in future work.

4. Analysis of mosquito population modelsHanna Reed

Abstract. An ODE mosquito population model is developed and expanded upon toinvestigate the dynamics of a Wolbachia infection in a mosquito population. In a bio-logically feasible situation, three equilibria are found and local stability is determined.Conditions under which a population of Wolbachia infected mosquitoes may persist in theenvironment are established via the next generation number.

MS20: Dynamics of Partial Differential Equations

Organizer: Xiaoying Han, Auburn University

Description: Structural and asymptotic properties of partial differential equations provide crucial in-sights in understanding physical phenomena governed by the equations. These includesome special structures, such as steady states, periodic and quasi-periodic solutions,chaotic orbits, as well as their qualitative properties like stability etc. In particular,the relationship between the qualitative structures and the regularity analysis of par-tial differential equations is an essential analytical aspect of partial differential equationdynamics. The stability and related dynamics have been a central problem in the area.Also, invariant structures such as invariant manifolds and attractors have been provedto be efficient to capture local and global dynamics, and to reduce dimensions. Thepurpose of this mini-symposium is to present newest results on theory and techniquesfor studying various dynamics of partial differential equations.

Talksdetails:

1. Global dynamics on 1D compressible MHDRonghua Pan, Georgia Institute of Technology

Abstract. Global dynamis of classical solutions of 1D Compressible MHD with largeinitial data has an interesting history and is challenging. We will report a recent progressmade by my joint work with X. Qin.

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2. The dynamical behavior of solutions of nonlocal partial differential equa-tionsXingjie Yan, China University of Mining and Technology

Abstract. In this talk, we study the partial differential equations with nonlocal operator.First, we introduce some results on the existence and multiplicity of solutions of ellipticpartial differential equations with nonlocal operator. Then we consider the dynamicalbehavior of solutions of parabolic equations with nonlocal operator, we will show thatthere indeed exists difference on the dynamical behavior of partial differential equationswith local and nonlocal operator.

3. Turning point principle for the stability of stellar modelsZhiwu Lin, Georgia Tech

Abstract. I will discuss some recent results (with Chongchun Zeng) on stability crite-rion for non-rotating gaseous stars modeled by the Euler-Poisson system. Under generalassumptions on the equation of states, we proved a turning point principle that the sta-bility of the stars is entirely determined by the mass-radius curve parametrized by thecenter density. In particular, the stability can only changed at points with an extremalmass. We use a combination of first order and 2nd order Hamiltonian formulations to getthe stability criterion and the semi-group estimates for the linearized equation.

4. Time periodic solutions to the full hydrodynamic model to semiconduc-torsMing Cheng, Jilin University

Abstract. A full hydrodynamic semiconductor model with a time periodic external forceis concerned. First, we regularize the system under consideration and prove the existenceof time periodic solutions to the linearized approximate system by applying Tychonofffixed point theorem combined with the energy method and the decay estimates. Thisidea is from the Massera-type criteria for linear periodic evolution equations. Then,the existence of a strong time periodic solution under some smallness assumptions isestablished by using the topological degree theory and an approximation scheme. Theuniqueness of time periodic solutions is proved basing on the energy estimates. Also, theexistence of the stationary solution is obtained.

CS: Contributed Session (Part I)


Talksdetails:

1. A fast delay Vandermonde solver for beamformingSirani M. Perera, Embry-Riddle Aeronautical University

Abstract. Delay Vandemonde matrix (DVM) is a superclass of discrete Fourier trans-form matrix having entries as the powers of delays based on multibeam beamforming. Thestructure of DVM can be utilized to realize as an analog circuit answering applications inwireless communication. In this talk, we will present a fast and exact algorithm to solvea system of linear equations having the coefficient matrix as the DVM with order 𝑛× 𝑛.

First, we present a sparse factorization to compute the inverse of the DVM efficiently.Then, we use the proposed factorization to derive a fast algorithm with the arithmeticcomplexity of order 𝒪(𝑛2) as opposed to 𝒪(𝑛3). Next, we present numerical results for theforward accuracy of the proposed algorithm with different delays. Finally, the languageof signal flow graph representation of digital structures is used to describe the proposedalgorithm.

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2. A fast hybrid transform algorithm for beam digitizationLevi Lingsch, Embry-Riddle Aeronautical University

Abstract. The process of digitization - the conversion of analog information into adiscrete signal - is essential to the function of millions of devices, from cell phones to par-ticle accelerators. This is what allows computers to understand and process the physicalworld. While short signals are easily processed, longer signals can require an exponentiallygrowing amount of computational operations. For this reason, it is necessary to developfast algorithms which can efficiently digitize large signals. Such algorithms will allow forthe production of less expensive yet more powerful computer circuitry that will open upstronger channels for communication and scientific discovery.

In this talk, we will observe a hybrid of discrete transform matrices and its sparse factor-ization to derive a fast algorithm. Next, the language of signal flow graphs will be utilizedto connect the algebraic operations associated with the proposed algorithm to realize thesystem as an integrated circuit. Finally, the proposed algorithm will be utilized to reducethe chip area and power consumption of analog to digital converter channels.

3. Resonant tori, transport barriers, and chaos in a vector field with aNeimark-Sacker bifurcationEmmanuel Fleurantin, Florida Atlantic University

Abstract. We make a detailed numerical study of a three dimensional dissipative vectorfield derived from the normal form for a cusp-Hopf bifurcation. The vector field exhibitsa Neimark-Sacker bifurcation giving rise to an attracting invariant torus. Our main goalsare to (A) follow the torus via parameter continuation from its appearance to its disap-pearance, studying its dynamics between these events, and to (B) study the embeddings ofthe stable/unstable manifolds of the hyperbolic equilibrium solutions over this parameterrange, focusing on their role as transport barriers and their participation in global bifur-cations. Taken together the results highlight the main features of the global dynamics ofthe system.

4. Clustering in sparse popularity adjusted stochastic block modeMajid Noroozi, University of Central Florida

Abstract. In the present talk, we introduce the Sparse Popularity Adjusted StochasticBlock Model (SPABM) which is a special case of the Popularity Adjusted Stochastic BlockModel (PABM). Since the real-life networks are usually sparse, studying a model that isdesigned to deal with such networks is very useful. One of the shortcomings of well-studiedblock models such as the SBM and the DCBM is that they do not allow to efficiently modelsparsity in networks, while the SPABM can be used to effectively model the sparsity byallowing a node to be inactive in some communities, yet active in the others. Clusteringis one of the fundamental problems in network analysis. To detect the communities in thenetworks that fit the SPABM, we propose to use a subspace clustering method. We alsoestimate the true number of communities in such networks using the estimated connectionprobabilities. Experiments on synthetic and real data sets demonstrate the effectivenessof the clustering and estimation approaches.

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5. Multiple linear regression: out-of-sample predictions with an examplein healthcare stocksPhong Luu, University of North Georgia

Abstract. We analyze the healthcare stocks and show high R-squared does not neces-sarily means high predictability. Moreover, we show multiple linear regression can helpus study the behavior of a data set and produce a model with high predictability. Inparticular, by learning the pattern of the near and far out-of-sample-prediction errors fordifferent time periods throughout a data set, we are able to use the near out-of-sampleprediction errors to control the prediction errors and identify a subset of predictors whichcan be used to build a high predictability model.

CS: Contributed Session (Part II)


Talksdetails:

1. Wide neural networks with bottlenecks are deep Gaussian processesDevanshu Agrawal, University of Tennessee Knoxville

Abstract. There has recently been much work on the "wide limit" of neural networks,where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process(GP) as all hidden layers are sent to infinite width. However, these results do not applyto architectures that require one or more of the hidden layers to remain narrow. In thiswork, we consider the wide limit of BNNs where some hidden layers, called "bottlenecks",are held at finite width. The result is a composition of GPs that we term a "bottleneckneural network Gaussian process" (bottleneck NNGP). Although intuitive, the subtletyof the proof is in showing that the wide limit of a composition of networks is in factthe composition of the limiting GPs. We also analyze theoretically a single-bottleneckNNGP, finding that the bottleneck induces dependence between the outputs of a multi-output network that persists through infinite post-bottleneck depth, and prevents thekernel of the network from losing discriminative power at infinite post-bottleneck depth.

2. Adversarial machine learning: error and sensitivity characterizationAlison Jenkins, Auburn University

Abstract. Adversarial machine learning defense techniques are enhanced using statis-tics and mathematics to develop error and sensitivity characterizations which inform thesystem. Error and sensitivity characterization are effective tools for informing both theimplementations and the design of adversarial machine learners in various fields. Applica-tions to technologies in medical and industrial robotics, autonomous vehicles, encryption,and cryptography are discussed.

An Adversarial System to attack and an Authorship Attribution System (AAS) to de-fend itself against the attacks are analyzed. Defending a system against attacks from anadversarial machine learner can be done by randomly switching between models for thesystem, by detecting and reacting to changes in the distribution of normal inputs, or byusing other methods. Adversarial machine learning is used to identify a system that isbeing used to map system inputs to outputs. Three types of machine learners are usingfor the model that is being attacked.

The machine learners that are used to model the system being attacked are a Radial BasisFunction Support Vector Machine, a Linear Support Vector Machine, and a FeedforwardNeural Network. The feature masks are evolved using accuracy as the fitness measure. Thesystem defends itself against adversarial machine learning attacks by identifying inputsthat do not match the probability distribution of normal inputs. The system also defendsitself against adversarial attacks by randomly switching between the feature masks beingused to map system inputs to outputs.

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3. Existence of a solution for a generalized Forchheimer flow in porousmediaThinh Kieu, University of North Georgia

Abstract. This paper is focused on the generalized Forchheimer flows for slightly com-pressible fluids, described as a system of two nonlinear degenerating partial differentialequations of first order. We prove the existence and uniqueness of the Dirichlet problemfor the stationary case. The technique of semidiscretization in time is used to prove theexistence for the time-dependent case

4. Optimizing numerical simulations of colliding galaxies I: theoretical andmathematical aspectsGraham West, Middle Tennessee State University

Abstract. Gravitational 𝑛-body models can be used to simulate the dynamical evolutionof colliding galaxies. Given observational data in the form of images of the galaxies,it is possible to estimate the true values of the various dynamical parameters throughthe careful application of optimization methods. However, the optimizing of such 𝑛-body models can be quite difficult for a number of reasons. First, full 𝑛-body codesare computationally expensive and the application of any optimization method requiresmany model runs. Second, due to the dimensionality and non-linearity of the system,the parameter space that must be explored is very complex. To address these challenges,we developed multi-factor fitness functions which are able to able to accurately performmorphological comparisons between model and target images. Using these functions, weapply a novel adaptive kernel mixing strategy which can be applied in both stochasticoptimization and Markov chain Monte Carlo contexts. Using simulated models withknown parameters as a surrogate for actual observational data, we test our fitness andoptimization techniques for robustness and accuracy. While this talk focuses primarilyon the theoretical and mathematical aspects of our research, the second will be directedtowards the application of these ideas to observational data.

5. Optimizing numerical simulations of colliding galaxies II: fitting simu-lations to astronomical dataMatthew Ogden, Middle Tennessee State University

Abstract. Our research is focused on determining the dynamical parameters associatedwith galaxy collisions that cannot be obtained via direct observation, such as orbital ve-locities, orientations, and mass-ratios between the galaxies. We are accomplishing thisby fitting numerical models of galactic interactions with astronomical observations of col-liding galaxies. To optimize our numerical models, our research group is working on twotasks. First, we develop computational methods for scoring the similarity between a galac-tic model and observed target galaxies. Second, we find the best models by optimizingthe parameters that characterize this nonlinear system using the machine scoring methodabove. This talk will focus on how we compare our numerical models to astronomicallyobserved colliding galaxies. To do so, gravitational n-body models are generated thatcapture the tidal distortions from galaxy collisions. The final particle positions are thenprocessed to create model images that have realistic intensity profiles and resolutions. Wecompare the model images with the astronomical images to obtain an objective machinescore that should reflect the fitness of the model. In order to test our scoring methods, wethen compare our machine scores to the human scores obtained from the citizen scienceproject Galaxy Zoo: Mergers.

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CS: Contributed Session (Part III)


Talksdetails:

1. A Formulation of the porous medium equation with time-dependentporosity: a priori estimatesKoffi Fadimba, University of South Carolina Aiken

Abstract. We consider a generalized form of the porous medium equation where theporosity 𝜑 is a function of time 𝑡: 𝜑 = 𝜑(𝑥, 𝑡):

𝜕(𝜑𝑆)

𝜕𝑡−∇ · (𝑘(𝑆)∇𝑆) = 𝑄(𝑆). (1)

Unlike many works in the literature where the porosity 𝜑 is either assumed to be inde-pendent of time or to depend very little of time variable 𝑡, we investigate the case whereit does depend on 𝑡 (and 𝑥 as well). We make a change of unknown function 𝑉 = 𝜑𝑆 toobtain a saturation-like (advection-diffusion) equation

𝜕𝑉

𝜕𝑡+∇ · (𝐹 (𝑉 )w)−∇ · (𝐷(𝑉 )∇𝑉 ) = �̃�(𝑉 ). (2)

A priori estimates and regularity results are established for (2) based in part on what isknown from the saturation equation, when 𝜑 is independent of the time 𝑡. These results arethen extended to the full saturation equation with time-dependent porosity 𝜑 = 𝜑(𝑥, 𝑡).

In this presentation, we concentrate on deriving regularity results and a priori estimatesfor the above described work.

2. An efficient numerical method for modeling electromagnetic wave scat-tering by random surfacesKelsey Ulmer, Auburn University

Abstract. We present an efficient numerical method for modeling the scattering ofelectromagnetic waves by a multiply layered material with random surfaces. We proposea combination of the Monte Carlo-Transformed Field Expansion Method with the use ofImpedance-Impedance Operators in the inner layers. The Monte Carlo-Transformed FieldExpansion Method achieves significantly reduced computational costs through a domainflattening change of variables, high order perturbation of surfaces expansions, and MonteCarlo sampling. The employment of Impedance-Impedance Operators avoids singularitiesthat typically arise from the more frequently used Dirichlet to Neumann Operators in theinner layers. This is collaborated work with Dr. Junshan Lin of Auburn University andDr. David Nicholls of the University of Illinois at Chicago.

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3. Stochastic gradient descent and adaptive gradient descent algorithms incontrol of stochastic partial differential equationsSomak Das„ Auburn University

Abstract. Most of our contemporary mathematical models are based on partial dif-ferential equations. However, the varied levels of randomness pose difficulties for suchsystems to be accurately modeled using deterministic partial differential equations. Insuch settings we use stochastic partial differential equations to incorporate the random-ness. To determine the optimal control for the stochastic system we adopt the stochasticgradient descent algorithm. With vast data-sets being customary for training of mostmachine learning algorithms, the stochastic gradient descent method is one of the effi-cient ways to obtain the optimal control. Another class of algorithms, adaptive gradientdescent, has also widespread applications in large scale stochastic optimizations. Thealgorithm adjusts its step-size at every iteration depending on the current gradient valueunlike stochastic gradient where we need to re-tune the step-size manually. In this talkwe show the results obtained from these algorithms.

4. Convective stability of carbon sequestration in porous mediumMahmoud DarAssi, Princess Sumaya University for Technology

Abstract. A simplified mathematical model for the interactions between the carbondioxide and brine in underground is considered. The linear stability is investigated. Thelong wavelength expansion method is applied to conduct the weakly nonlinear stabilityanalysis. The evolution equation is derived and analyzed. A uniformly valid periodicsolution of the evolution equation is obtained by the application of Poincare-Lindstedtmethod. Some numerical simulations is presented.

5. Conservation laws in heterogenous mediaBaris Kopruluoglu, Auburn University

Abstract. Conservation laws play an important role in many areas of natural science.When we design numerical schemes for conservation laws, we usually assume that initialdata and flux function (the rate of change of quantity of interest) are known exactly.However, this is generally not the case as these are often obtained through indirect mea-surements. As a consequence the initial data and flux function are known only in termsof statistical quantities like mean, variance and involve someuncertainty. These uncertaininputs should be handled statistically. In our study, we analyze and implement the MonteCarlo finite volume method and the stochastic nite volume Method to solve conservationlaws in random media. Our simulations include that of the inviscid Burgers equation withrandom inputs.

6. Quantitative analysis of scattering resonances for a 3D subwavelengthcavityMaryam Fatima, Auburn University

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