{"ID":2887396,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.01854","arxiv_id":"2508.01854","title":"Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures","abstract":"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.","short_abstract":"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 t...","url_abs":"https://arxiv.org/abs/2508.01854","url_pdf":"https://arxiv.org/pdf/2508.01854v2","authors":"[\"Fanze Kong\",\"Chen-Chih Lai\",\"Yubin Lu\"]","published":"2025-08-03T17:11:41Z","proceeding":"physics.comp-ph","tasks":"[\"physics.comp-ph\",\"cs.LG\",\"math.AP\",\"nlin.AO\"]","methods":"[\"Diffusion Model\"]","has_code":false}