Post on 26-Mar-2022
The Glotzer Group @ University of Michigan
Mmm: cats!Modeling molecular motion:
complex adaptive thermodynamic simulations
Eric JankowskiGlotzer Group
CSAAW talk 1-19-2007
The Glotzer Group @ University of Michigan
A tale of two talks:
• ABM’s and potential energy minimization: can “learning” be used to speed up simulations?
• Self-assembly and switchability: can we figure out what properties particles need to robustly assemble a desired structure?
The Glotzer Group @ University of Michigan
Nanoscale simulation
• Want to predict what structures will form, given a set of particles and interactions
• Want to ask “How do I assemble __?”
• Many methods to do this: molecular dynamics, Brownian dynamics
• If all you care about is equilibrium structure, then Monte Carlo is method of choice
The Glotzer Group @ University of Michigan
Monte Carlo basics
• Find free energy minima by randomly changing configurations in a smart way
• Uphold detailed balance
• P(A)*P(A->B)=P(B)*P(B-A)
• Ensures that the chain of states moves towards equilibrium, and stays there
The Glotzer Group @ University of Michigan
Agent-based modeling
• Bread and butter for many CSCS students
• Strength is in hypothesis testing
• Simple premise:
• Define agents, interactions
• Define environment
• See what happens!
The Glotzer Group @ University of Michigan
Ratner et al.
• Model designed to simulate charged molecules such as polymers.
• Agents are “Tetris” pieces made up of three types of cells.
Ratner, Troisi, Wong 2004Note, cell colors not equivalent
Interaction energies:
The Glotzer Group @ University of Michigan
Learning algorithm
• Goal is to bias energetically favorable structures
• Particles form clusters with most attractive neighbor
• These clusters are sorted by size
• Best energy for each cluster size is recorded
The Glotzer Group @ University of Michigan
Learning algorithm
• Cluster energies are checked against tabulated values
• If they are the best cluster of that size, they move as a cluster
• If not, the cluster breaks up into individual particles
The Glotzer Group @ University of Michigan
Ratner’s results
• Learning algorithm finds energy minimizing structures in fewer time steps than Monte Carlo
• Finds better structures (energy 15% lower)
Ratner, Troisi, Wong 2004
The Glotzer Group @ University of Michigan
...but there are some problems
• No discussion of temperatures
• Critical for comparing energies
• Disobeys detailed balance
• Clock cycles/real time, not timesteps, are the performance indicator
• Does learning speed up a cluster Monte Carlo code?
The Glotzer Group @ University of Michigan
Investigate effect of learning
• Reproduce Ratner’s system, compare cluster Monte Carlo with and without learning
• What to look for:
• Best structure in each simulation
• How long it took to find the structure
The Glotzer Group @ University of Michigan
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The Glotzer Group @ University of Michigan
Discussion
• Learning doesn’t help
• Prevents “almost as good” clusters
• Different learning schemes could do better, but they’re all non-physical
• ABM’s good for exploring systems that aren’t understood
Learning No learning
The Glotzer Group @ University of Michigan
Future work
• Make a better learning algorithm, compare clock cycles
• Use a genetic algorithm to search configuration space
• Explore 3D systems
• Add “state” variables, and keep learning Markovian
• Chat with the man himself
The Glotzer Group @ University of Michigan
Lattice + 2D = 2plane
• Real systems are often far from equilibrium
• What about systems of particles with adaptive interactions?
• Want to figure out what properties a set of particles needs to form a target structure: transistor, synthetic capsid, spiraling swarm
The Glotzer Group @ University of Michigan
Why model switchable cubes?
• Experimentalists improving control over particle morphology
• Switchable surfaces have been developed
• Base model for proteins, nanobots, not-so-nano bots
Au
Obare & MurphyNano Letters, 2001
Kotov, Pre-print
Y particle
The Glotzer Group @ University of Michigan
Inspiration: Poulton et al.
• Model a system of homogenous agents whose states can switch
• Like proteins or nanoparticles that change shape or charge when something binds to it
Poulton et al, 2005.
The Glotzer Group @ University of Michigan
The idea:
• Make a Brownian dynamics simulation of cubes
• Make the cubes switchable
• Pick some nice structures to form
• Use a GA to find rule sets that make them
• Tell experimentalists what they need to do
• Throw fistfuls of money in the air
The Glotzer Group @ University of Michigan
The Simulation
• Approximate cubes with 14 spheres
• “face” spheres can change their interaction potentials
• Choice of interaction potentials important
The Glotzer Group @ University of Michigan
Changing faces
• Rules encoded as strings
• Positive=1, Negative=-1, Neutral=0, “don’t care” = #
• (#,0,-1,#,#,#)@(#,#,1,#,#,#)->(#,#,#,#,#,1) means “if my 2nd face is neutral, 3rd is negative, and a positive face is stuck to my third face, change my 6th face to positive”
• Easy to manipulate, large rule space (68 billion rules, way more combinations of rules)
The Glotzer Group @ University of Michigan
What to make?
• The letter “T”
• A box
• A cycling swarm
• The snag: defining a fitness function for each structure
The Glotzer Group @ University of Michigan
Computational Challenges
• Say it takes 3 hours to run a million time steps
• Need to run ~50 simulations per GA generation
• Need to run lots of GA generations...
The Glotzer Group @ University of Michigan
In the meantime...
• Very interesting to look at how adaptive particles behave
• Use some Intelligent Design to make some basic structures
• Can use same ideas, applied to interaction potentials
The Glotzer Group @ University of Michigan
The end, kinda
• ABM’s can be very useful in studying molecular self-assembly
• Should be used to model the way you think things might behave
• Lots to be learned, so this is just the beginning of the story