{"ID":2876300,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.10495","arxiv_id":"2509.10495","title":"Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts","abstract":"Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift decompositions in generalized diffusion systems involving conservative-dissipative dynamics. The method is robust to noisy data, adaptable to rough potentials and oscillatory rotations. We demonstrate its effectiveness through several numerical experiments.","short_abstract":"Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift decompositions in generalized diffusion systems involving conservative-dissipative dynamics. The method is robust to noisy data, adaptable...","url_abs":"https://arxiv.org/abs/2509.10495","url_pdf":"https://arxiv.org/pdf/2509.10495v1","authors":"[\"Fanze Kong\",\"Chen-Chih Lai\",\"Yubin Lu\"]","published":"2025-08-31T16:51:29Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"physics.comp-ph\"]","methods":"[\"Diffusion Model\"]","has_code":false}