PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning
Feng Liu Faguo Wu Xiao Zhang
The normalization constraint on probability density poses a significant
challenge for solving the Fokker-Planck equation. Normalizing Flow, an
invertible generative model leverages the change of variables formula to ensure
probability density conservation and enable the learning of complex data
distributions. In this paper, we introduce Physics-Informed Normalizing Flows
(PINF), a novel extension of continuous normalizing flows, incorporating
diffusion through the method of characteristics. Our method, which is mesh-free
and causality-free, can efficiently solve high dimensional time-dependent and
steady-state Fokker-Planck equations.