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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.01854 |
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| _version_ | 1866909729279705088 |
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| author | Kong, Fanze Lai, Chen-Chih Lu, Yubin |
| author_facet | Kong, Fanze Lai, Chen-Chih Lu, Yubin |
| contents | This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment evolution, we design a two-stage method to recover the pseudo-potential and rotation in the pointwise orthogonal decomposition of a class of non-gradient drifts in generalized diffusions. Our two-stage method is applied to complex generalized diffusion processes including dissipation-rotation dynamics, rough pseudo-potentials and noisy data. Representative numerical experiments demonstrate the effectiveness of our approach for learning physical laws in non-gradient generalized diffusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures Kong, Fanze Lai, Chen-Chih Lu, Yubin Computational Physics Machine Learning Analysis of PDEs Adaptation and Self-Organizing Systems This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment evolution, we design a two-stage method to recover the pseudo-potential and rotation in the pointwise orthogonal decomposition of a class of non-gradient drifts in generalized diffusions. Our two-stage method is applied to complex generalized diffusion processes including dissipation-rotation dynamics, rough pseudo-potentials and noisy data. Representative numerical experiments demonstrate the effectiveness of our approach for learning physical laws in non-gradient generalized diffusions. |
| title | Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures |
| topic | Computational Physics Machine Learning Analysis of PDEs Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2508.01854 |