Mmm: cats! Modeling molecular motion: complex adaptive thermodynamic simulations. Eric Jankowski Glotzer Group CSAAW talk

Transcription

1 Mmm: cats! Modeling molecular motion: complex adaptive thermodynamic simulations Eric Jankowski Glotzer Group CSAAW talk

2 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?

3 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

4 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

5 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!

6 Ratner et al. Model designed to simulate charged molecules such as polymers. Agents are Tetris pieces made up of three types of cells. Interaction energies: Ratner, Troisi, Wong 2004 Note, cell colors not equivalent

7 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

8 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

9 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

10 ...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?

11 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

12 Results Potential Energy Time steps elapsed when best structure found With Learning Maximum Cluster Size with learning Without Learning Maximum Cluster Size without learning

13 Discussion Learning doesn t help Prevents almost as good clusters Learning No learning Different learning schemes could do better, but they re all non-physical ABM s good for exploring systems that aren t understood

14 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

15 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

16 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 & Murphy Nano Letters, 2001 Y particle Kotov, Preprint

17 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.

18 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

19 The Simulation Approximate cubes with 14 spheres face spheres can change their interaction potentials Choice of interaction potentials important

20 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)

21 What to make? The letter T A box A cycling swarm The snag: defining a fitness function for each structure

22 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...

23 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

24 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