Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks

TL;DR

This paper demonstrates that Deep Generative Adversarial Networks can effectively learn and simulate stochastic kinetic dynamics in complex systems, providing accurate, computationally efficient surrogates for traditional models.

Contribution

The study introduces a novel application of GANs to learn kinetic Monte Carlo dynamics, enabling faster stochastic simulations with high accuracy and discussing model modifications for improved convergence.

Findings

GANs can reproduce equilibrium and kinetic properties within a few percent accuracy.

The method reduces computational costs compared to traditional Kinetic Monte Carlo simulations.

The approach effectively captures surface fluctuation dynamics in a multi-particle system.

Abstract

We show that Generative Adversarial Networks (GANs) may be fruitfully exploited to learn stochastic dynamics, surrogating traditional models while capturing thermal fluctuations. Specifically, we showcase the application to a two-dimensional, many-particle system, focusing on surface-step fluctuations and on the related time-dependent roughness. After the construction of a dataset based on Kinetic Monte Carlo simulations, a conditional GAN is trained to propagate stochastically the state of the system in time, allowing the generation of new sequences with a reduced computational cost. Modifications with respect to standard GANs, which facilitate convergence and increase accuracy, are discussed. The trained network is demonstrated to quantitatively reproduce equilibrium and kinetic properties, including scaling laws, with deviations of a few percent from the exact value. Extrapolation limits and future perspectives are critically discussed.