Learning Neural Pushforward Samplers for Distributions from Fokker-Planck Equations by Weak Adversarial Training
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915548115238912 |
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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 |