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Autores principales: He, Andrew Qing, Cai, Wei
Formato: Preprint
Publicado: 2025
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Acceso en línea:https://arxiv.org/abs/2509.14575
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author He, Andrew Qing
Cai, Wei
author_facet He, Andrew Qing
Cai, Wei
contents This paper presents a new method for solving Fokker-Planck equations (FPE) by learning a neural sampler for the distribution given by the FPE via an adversarial training based on a weak formulation of the FPE where the adjoint operator of FPE acts on the test function. Such a weak formulation transforms the PDE solution problem into a Monte Carlo importance sampling problem where the FPE solution-distribution is learned through a neural pushforward map, avoiding some of the limitations of direct PDE based methods. Moreover, by using simple plane-wave test functions, derivatives on the test functions can be explicitly computed. This approach produces a natural importance sampling strategy for the FPE solution distribution with probability conservation, from which the FPE solution can be easily constructed.
format Preprint
id arxiv_https___arxiv_org_abs_2509_14575
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Learning Neural Pushforward Samplers for Distributions from Fokker-Planck Equations by Weak Adversarial Training
He, Andrew Qing
Cai, Wei
Numerical Analysis
65N75, 68T07, 35Q84
This paper presents a new method for solving Fokker-Planck equations (FPE) by learning a neural sampler for the distribution given by the FPE via an adversarial training based on a weak formulation of the FPE where the adjoint operator of FPE acts on the test function. Such a weak formulation transforms the PDE solution problem into a Monte Carlo importance sampling problem where the FPE solution-distribution is learned through a neural pushforward map, avoiding some of the limitations of direct PDE based methods. Moreover, by using simple plane-wave test functions, derivatives on the test functions can be explicitly computed. This approach produces a natural importance sampling strategy for the FPE solution distribution with probability conservation, from which the FPE solution can be easily constructed.
title Learning Neural Pushforward Samplers for Distributions from Fokker-Planck Equations by Weak Adversarial Training
topic Numerical Analysis
65N75, 68T07, 35Q84
url https://arxiv.org/abs/2509.14575