# Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2507.21763 · HTML: https://mlsanity.com/paper/2507.21763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 65 references that are in the map.
- First posted on arXiv 29 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [A high-bias, low-variance introduction to Machine Learning for physicists](https://mlsanity.com/paper/1803.08823/) (2018)
- [Rethinking materials simulations: Blending direct numerical simulations with neural operators](https://mlsanity.com/paper/2312.05410/) (2023)
- [Deep learning for synthetic microstructure generation in a materials-by-design framework for heterogeneous energetic materials](https://mlsanity.com/paper/2004.04814/) (2020)
- [Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model](https://mlsanity.com/paper/2310.01678/) (2023)
- [Microstructure Generation via Generative Adversarial Network for Heterogeneous, Topologically Complex 3D Materials](https://mlsanity.com/paper/2006.13886/) (2020)
- [SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics](https://mlsanity.com/paper/2302.03663/) (2023)
- [Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired Neural Networks for the 3D microstructure evolution of materials via Cahn-Hilliard flow](https://mlsanity.com/paper/2407.20126/) (2024)
- [Accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networks](https://mlsanity.com/paper/2305.15920/) (2023)

## 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.