Machine learning stochastic dynamics

Stochastic dynamics is widely used in physics, chemistry, biology, and other fields. For the study of high-dimensional stochastic dynamical systems, traditional numerical methods encounter the problem of high computational complexity or insufficient precision. In recent years, machine learning methods have provided new approaches to such problems. This article will review the progress of machine learning applications in stochastic dynamical systems. For stochastic dynamics with discrete state variables, variational autoregressive neural networks can help efficiently calculate the free energy, evolution of probability distribution, and dynamical phase transition. The method is suitable for classical and quantum spin systems and chemical reaction networks. For continuous state variables, machine learning methods such as reservoir computing and flow models can learn and predict noise-induced phenomena of stochastic differential equations and the evolution of partial differential equation systems. These applications provide a paradigm for machine learning in stochastic dynamics and inspire more applications of artificial intelligence in scientific fields.