Bridging simulation length scales with cellular automata

Abstract

Multiscale simulation requires coupling physics models that operate at different characteristic length and time scales, because no single method spans the range needed for most problems of interest. Moving to a coarser-grained representation unlocks longer length and time scales, but it discards the microscopic interactions that build morphology. A fine-grained model can be initialized from an arbitrary packing and left to self-assemble into a physically meaningful structure; a lower-resolution model cannot, and must inherit its starting configuration from a higher-fidelity simulation. The length scales accessible to the coarse-grained model are therefore set not by the coarse-grained method itself, but by the largest fine-grained configuration that can be affordably equilibrated. A representative example is the scale-up from particle-based molecular dynamics (MD) to a lattice-based representation such as kinetic Monte Carlo (kMC). In this work, we present a cellular automata (CA) approach for generating arbitrarily large lattice starting configurations. CA is a natural fit for this task: short-ranged local rules drive the evolution of a lattice, and their repeated application gives rise to emergent long-range order, thematically mirroring how short-ranged interactions in MD produce self-assembled morphology. We use a configuration from a higher-fidelity simulation as a training set and learn the CA rules from it via logistic regression. As a proof of principle, we develop these rules for a hydrated anion exchange membrane (AEM), generate new starting configurations, and benchmark their performance in mesoscale kMC simulations against an MD-derived "ground truth." We then demonstrate the ability to generate substantially larger lattices and show that their behavior in kMC is consistent with that of the smaller CA benchmark configurations.