Solving Time Dependent Fokker-Planck Equations via Temporal Normalizing Flow

In this work, we propose an adaptive learning approach based on temporalnormalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It iswell known that solutions of such equations are probability density functions, and thusour approach relies on modelling the target solutions with the temporal normalizingflows. The temporal normalizing flow is then trained based on the TFP loss function,without requiring any labeled data. Being a machine learning scheme, the proposedapproach is mesh-free and can be easily applied to high dimensional problems. Wepresent a variety of test problems to show the effectiveness of the learning approach.