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.

翻译：本文证明，生成对抗网络（GANs）可有效用于学习随机动力学，在捕捉热涨落的同时替代传统模型。具体而言，我们展示了该方法在二维多粒子系统中的应用，重点关注表面台阶涨落及其相关的时间依赖粗糙度。基于动力学蒙特卡洛模拟构建数据集后，我们训练了一个条件GAN来随机传播系统状态随时间演化，从而能够以较低计算成本生成新序列。文中讨论了针对标准GAN的改进措施，这些改进有助于提升收敛性并提高精度。经训练的网络被证明能够定量复现平衡态与动力学性质（包括标度律），其与精确值的偏差在百分之几以内。本文还对方法的推断局限性及未来发展方向进行了批判性讨论。