2023/09/26 by Feng Liu, Liu, Feng, Faguo Wu +3
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2309.15139
openalex publication_date 2023/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.