PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning

• URL: http://arxiv.org/abs/2309.15139v1
• Date: Tue, 26 Sep 2023 15:38:57 GMT
• Title: PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning
• Authors: Feng Liu, Faguo Wu and Xiao Zhang
• Abstract summary: In this paper, we introduce Physics-Informed Normalizing Flows (PINF), a novel extension of continuous normalizing flows. Our method, which is mesh-free and causality-free, can efficiently solve high dimensional time-dependent and steady-state Fokker-Planck equations.
• Score: 8.000355537589224
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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