Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks

Stochastic evolution laws are a key ingredient to simulate many processes of both fundamental and applied interest in condensed matter physics, materials science and engineering. Fluctuations are central for a proper description of non-equilibrium processes such as nucleation and growth, roughening of free surfaces, rare or activated events and phase transitions [1-5], to cite a few examples. Too coarse approximations of the involved probability distributions lead to inaccurate computational models that are unable to quantitatively reproduce experimental reality. On the other hand, more accurate approaches, such as molecular dynamics (MD) [6, 7] and Kinetic Monte Carlo (KMC) [8-10], may be limited in the possibility of reaching realistic temporal and spatial scales. In recent years, machine learning (ML) has emerged as a new tool to infer probability distributions from data in several fields, allowing for the automatic extraction of correlations between observations [11, 12]. Generative models in particular deal with the task of obtaining ML tools capable of generating new samples from a distribution given only samples extracted from it [13]. Among these approaches, Generative Adversarial Networks (GANs) [14] have already proven outstanding capabilities in several fields, e.g,.