Solving time dependent Fokker-Planck equations via temporal normalizing flow

The Fokker-Planck (FP) equations, which describe the time evolution of probability density functions (PDFs) of complex stochastic systems, have been widely used in different fields such as physical and biological modelling[31][34]. Solving the FP equations numerically has been an important research topic in the past few decades. Generally, there are two main ways to obtain the PDFs of stochastic dynamics: solving the FP equations directly, or evaluating the transition probability density of the associated stochastic differential equations(SDEs). Traditional numerical methods for doing this include the finite element methods [4], the finite difference methods [19], the path integral methods [37], to name just a few. One of the biggest difficulties of these approaches is that either discretizition of a high dimensional (unbounded) physical space is needed, or a large number of sample paths via Monte Carlo method [12] should be used. In recent years, machine learning techniques have been widely used to solve partial differential equations (PDEs), see e.g.