Solving time dependent Fokker-Planck equations via temporal normalizing flow
This work addresses computational challenges in physics and engineering by providing a machine learning-based solution for high-dimensional PDEs, though it appears incremental as it adapts existing normalizing flow methods to a specific equation type.
The authors tackled solving time-dependent Fokker-Planck equations by proposing an adaptive learning approach using temporal normalizing flows, which is mesh-free and applicable to high-dimensional problems, demonstrating effectiveness through various test cases.
In this work, we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that solutions of such equations are probability density functions, and thus our approach relies on modelling the target solutions with the temporal normalizing flows. The temporal normalizing flow is then trained based on the TFP loss function, without requiring any labeled data. Being a machine learning scheme, the proposed approach is mesh-free and can be easily applied to high dimensional problems. We present a variety of test problems to show the effectiveness of the learning approach.