Phys516: Methods of Computational Physics

Aiichiro NakanoCollaboratory for Advanced Computing & Simulations

Department of Physics & AstronomyDepartment of Computer Science

Department of Chemical Engineering & Materials ScienceDepartment of Biological SciencesUniversity of Southern California

Email: anakano@usc.edu

Computational Physics Approach

Physical phenomenon

Mathematical model

Discrete algebraic approximation

Numerical algorithms

Simulation program

Computer experiment

Nature to Math to Computing

http://www.griffithobs.org

Universarium

Mathematical Model

Calculus-Based Science

http://research.microsoft.com/towards2020science

Calculus has been the principal scientific paradigm for 400 years

What’s Now? Physics in 100 Years• Increasingly, the development of algorithms will become a central focus

of theoretical physics. ... Triumphs of creative understanding such as universality (suppression of irrelevant details), symmetry (informed iteration), and topology (emergence of discrete from continuous) are preadapted to algorithmic thinking.

• The work of designing algorithms can be considered as a special form of teaching, aimed at extremely clever but literal-minded and inexperienced students—that is, computers—who cannot deal with vagueness. At present those students are poorly motivated and incurious, but those faults are curable. Within 100 years they will become the colleagues and ultimately the successors of their human teachers, with a distinctive style of thought adapted to their talents.

• Two developments will be transformative: naturalized artificial intelligence and expanded sensoria.

F. Wilczek, Phys. Today 69(4), 32 (’16)

Understanding Simple Math In your own words

Richard Feynman “On His Father’s Lap”http://onegoodmove.org/1gm/1gmarchive/2006/04/on_his_fathers.html

• Newton’s equation of motion

• Many-body interatomic potential

• Application: drug design, robotics, entertainment, etc.

Molecular Dynamics Simulation

A scene from the movie “Twister”

Cancer Modeling

Pedestrian Crowd Dynamics

See also http://www.oasys-software.com/products/engineering/massmotion.html

Nature 407, 487 (’00)

Computational Physics Approach

Physical phenomenon

Mathematical model

Discrete algebraic approximation

Numerical algorithms

Simulation program

Computer experiment

MD AlgorithmTime discretization: differential ® algebraic equation

ri(0)

ri(2Δ)ri(Δ)

Time stepping: Velocity Verlet algorithmGiven1. Compute as a function of2.3.4. Compute as a function of5.

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{! r i (t)}

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! a i (t)

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! v i (t +Δ2)← ! v i (t) +

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! a i (t + Δ)

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{! r i (t + Δ)}

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! v i (t + Δ)← ! v i (t +Δ2) +

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! r i (t),! v i (t)( )

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! r i (t + Δ) = ! r i (t) + ! v i (t)Δ +12! a i (t)Δ

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! v i (t + Δ) = ! v i (t) +! a i (t) + ! a i (t + Δ)

2Δ

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! a i = −1

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Computational Physics Approach

Physical phenomenon

Mathematical model

Discrete algebraic approximation

Numerical algorithms

Simulation program

Computer experiment

MD Program

// r[][] ® ra[][]

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! v i (t +Δ2)← ! v i (t) +

Δ2! a i (t)

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! r i (t + Δ)← ! r i (t) + ! v i (t +Δ2)Δ

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! v i (t + Δ)← ! v i (t +Δ2) +

Δ2! a i (t + Δ)

Computational Physics Approach

Physical phenomenon

Mathematical model

Discrete algebraic approximation

Numerical algorithms

Simulation program

Computer experiment

Computer Experiment

• Water nanojet formation and its collision with silica surface

• Billion-atom reactive MD simulation of shock-induced nanobubble collapse in water near silica surface (67 million core-hours on 163,840 Blue Gene/P cores)

A. Shekhar et al., Phys. Rev. Lett. 111, 184503 (’13)

Type of Mathematical Models Discrete/particle model (ordinary

differential equations) Continuum model (partial differential equations)

Deterministic molecular dynamics computational fluid dynamics, continuum mechanics

Stochastic Monte Carlo particle simulation quantum Monte Carlo

Shear stress (GPa)

Particle model of oxidation Continuum model of fracture

-0.8 0 0.8

Continuum Model: Quantum Mechanics

Density functional theory (DFT)(Walter Kohn, Nobel Chemistry Prize, ’98)

O(CN )

O(N3 )

Challenge: Complexity of quantum N-body problem

€

E ψn{ }[ ] = d3r∫ ψn*(r) − !

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∂2

∂r2+Vion (r)

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' (

)

* + ψn(r)

n=1

Nel∑ +

e2

2d3rd3 - r ρ(r)ρ( - r )

r − - r ∫∫ + EXC ρ(r)[ ]

Minimize:

with orthonormal constraints:

Charge density:

Constrained minimization problem:

𝜓(𝐫$, 𝐫&, … , 𝐫()*)

𝜓, 𝐫 |𝑛 = 1,… ,𝑁23

Walter Kohn (1923-2016)

Multiscale Modeling

A. Warshel & M. Karplus, J. Am. Chem. Soc. 94, 5612 (’72)A. Warshel & M. Levitt, J. Mol. Biol. 103, 227 (’76)

QM/MM:quantum-

mechanical/molecular-mechanical modeling

MD FED

QM O

QM Si Handshake H

MD Si

QM clusterQMD

Adaptive Multiscale Dynamics

QM/MD/FE:quantum mechanical/molecular-dynamics/

finite-element simulation

Oxidation of SiS. Ogata et al., Comput. Phys. Commun. 138, 143 (’01)L. Lidorikis et al., Phys. Rev. Lett. 87, 086104 (’01)

High-energy beam oxidation of Si (SIMOX)

H. Takemiya et al., IEEE/ACM Supercomputing (SC06)

Nonadiabatic Quantum Molecular Dynamics

• Excited states: Linear-response time-dependent density functional theory [Casida, ’95] • Interstate transitions: Surface hopping [Tully, ’90]

W. Mou et al., Appl. Phys. Lett. 98, 113301 (’11); ibid. 100, 203306 (’12); J. Chem. Phys. 136, 184705 (’12); Comput. Phys. Commun. 184, 1 (’13); Appl. Phys. Lett. 102, 093302 (’13); ibid. 102, 173301 (’13); J. Chem. Phys. 140, 18A529 (’14); IEEE Computer 48(11), 33 (’15); Sci. Rep. 5, 19599 (’16)

Zn porphyrin Rubrene/C60

quasi-electron; quasi-hole

Hydrogen Production from Water• 16,611-atom quantum MD simulation of rapid H2 production from water

using a LiAl particle on 786,432 Blue Gene/Q cores

K. Shimamura et al., Nano Lett. 14, 4090 (’14)

Stochastic Model of Stock PricesFluctuation in stock price

Technology Stock Basket Performance

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63-Stock BasketS&P 500 NASDAQ

Computational stock portfolio trading

Andrey Omeltchenko (Quantlab)

Basis of Black-Scholesanalysis of option prices

(1997 Nobel Economy Prize to Myron Scholes)

Monte Carlo Simulation

Random trial ® acceptance by a cost criterion

Monte Carlo

Moleculardynamics

Phys516: What You Will Learn

The ability to implement the solution of mathematically formulated problems on a computer

Computational physicists’ survival kit• Mathematical methods in physics: Any book you are familiar

with, e.g., G. B. Arfken & H. J. Weber, Mathematical Methods for Physicists, 7th Ed. (Academic Press, ’12)

• Numerical algorithms: W. H. Press, B. P. Flannery, S. A. Teukolsky, & W. T. Vetterling, Numerical Recipes, 3rd Ed. (Cambridge U Press, ’07)—available onlineC: www.nrbook.com/a/bookcpdf.phpFortran: www.nrbook.com/a/bookfpdf.phpFortran90: www.nrbook.com/a/bookf90pdf.php

Nature to math to computing!

You understand it = you can program it

Phys516: Computational Methods in the Context of Simulations

MSCS-HPCS: High-Performance Computing & Simulations

• A physics Ph.D. student can apply for admission into MSCS-HPCS after taking 3 CS500+ courses

A total of 32 units1. Required Core Courses in Computer Science: 3 courses

(a) CSCI570 (analysis of algorithms)(b) 2 from: CS561 (artificial intelligence), CS 571 (Web), CS585 (database)

2. Required Core Course for MSCS-HPCS:CSCI596 (scientific computing & visualization)

3. Elective Courses for MSCS-HPCS: Total of 3 courses from both tracks (a) & (b)(a) Computer Science TrackCSCI653 (high performance computing & simulations),CS503 (parallel programming), CS520 (animation), CS551 (communication), CS558L (network), CS580 (graphics), CS583 (comp geometry), CS595 (advanced compiler), EE653 (multithreaded arch), EE657 (parallel processing), EE659 (network), Math/CS501 (numerical analysis)(b) Computational Science/Engineering Application TrackAME535 (comp fluid dynamics), CE529 (finite element), CHE502 (numerical transport),EE553 (comp optimization), MAS575 (atomistic simulation), PTE582 (fluid flow),Phys516 (computational physics), ...

National Strategic Computing Initiative• July 29, 2015: President Obama issued an executive order

• NSCI will merge exaflop/s (1018 floating-point operations per second) high performance computing (HPC) & exabyte (1018 bytes) ‘big data’ to advance the frontier of sciences, economic growth, & national security

Big DataHPC

http://rebootingcomputing.ieee.org

• cf. IEEE rebooting computing initiative

MAterials Genome Innovation for Computational Software

Priya Vashishta-PI, Malancha Gupta, Rajiv K. Kalia, Aiichiro Nakano, Oleg Prezhdo University of Southern California

Uwe Bergmann and David Fritz Linac Coherent Light Source, SLACWilliam A. Goddard, III California Institute of TechnologyKristin A. Persson Lawrence Berkeley National Laboratory

David J. Singh University of MissouriPulickel M. Ajayan Rice University

Basic Energy Sciences

https://magics.usc.edu

Computational Synthesis of Functional Layered Materials: MAGICS Software Stack

Extensibleplug-ins –

Computationalsynthesis

Corelibraries –

Elementary processes

Current/future platforms

2

3

Scalable simulation engines

X-ray free-electron laser

1

INCITE|AURORA–MAGICS–LCLS Synergy

Linac CoherentLightSource

World’s first free-electron X-ray laser

HOMO LUMO

DOEINCITE&AuroraESPAwards

INCITE/Aurora ESP-SLAC Synergy

M.F. Lin et al., Nature Commun. 8, 1745 (’17)

• In the ultrafast ‘electron camera’, laser light hitting a material is almost completely converted into nuclear vibrations — key to switching material properties on & off at will for future electronics applications

• High-end quantum simulations reproduce the ultrafast energy conversion at exactly the same space & time scales, & explain it as a consequence of photo-induced phonon softening

Semiconductor-to-Metal Transition via Doping

V. Kochat et al., Adv. Mater. 29, 1703754 (’17)

• Experiment at Rice shows 2H-to-1T’ phase transformation by alloying MoSe2with Re

• QMD simulations at USC elucidate its electronic origin

• Simulation & experiment show novel magnetism centered at Re atoms

SeMoRe

spin up

spin down

2H

1T’