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Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks

arXiv 2507.21763 ↗First posted 29 Jul 2025cond-mat.stat-mech cond-mat.mtrl-sci cs.AIcited by 0

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Abstract (arXiv)

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.

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References · 14

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
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  10. 2023Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion modelcited by 16
  11. 2020Microstructure Generation via Generative Adversarial Network for Heterogeneous, Topologically Complex 3D Materialscited by 12
  12. 2023SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamicscited by 4
2 more
  1. 2024Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired Neural Networks for the 3D microstructure evolution of materials via Cahn-Hilliard flowcited by 4
  2. 2023Accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networkscited by 1

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