Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks

2025-07-29

AI Summary

Traditional kinetic Monte Carlo (kMC) simulations of surface step fluctuations and roughness evolution in two-dimensional many-particle systems suffer from prohibitive computational cost. To address this, we propose an enhanced conditional generative adversarial network (cGAN) framework that directly learns stochastic dynamics and models thermal fluctuations. Conditioned on discrete time steps and initial configurations, the model generates physically consistent surface evolution sequences end-to-end, preserving statistical properties such as height distribution, correlation functions, and scaling exponents. Experiments demonstrate that predicted dynamic scaling behaviors—including growth exponents and correlation length scaling—agree quantitatively with theoretical predictions and kMC benchmarks (error < 5%), accurately reproducing both equilibrium and nonequilibrium scaling laws. Moreover, inference is accelerated by two to three orders of magnitude relative to kMC, while maintaining strong generalization beyond training regimes. The method thus offers a computationally efficient, physically faithful surrogate for multiscale surface evolution modeling.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Cognitive Modeling & Cognitive Systems: Computational Creativity

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Learning stochastic dynamics using GANs to replace traditional models
• Reducing computational cost for simulating many-particle systems
• Quantitatively reproducing equilibrium and kinetic properties accurately

Innovation

• GANs learn stochastic dynamics efficiently
• Conditional GAN reduces computational cost
• Modified GANs improve accuracy significantly