PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning

Feng Liu, Faguo Wu, Xiao Zhang

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: Continuous normalizing flows, Fokker-Planck equations, ordinary differential equations, normalization constraint

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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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Submission Number: 3627