PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning
This addresses a challenge in physics-constrained deep learning for researchers in computational physics and machine learning, but appears incremental as an extension of existing normalizing flows.
The paper tackled solving the Fokker-Planck equation by introducing Physics-Informed Normalizing Flows (PINF), a mesh-free and causality-free method that efficiently handles high-dimensional time-dependent and steady-state cases.
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.