Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 36 of its 67 references that are in the map. First posted on arXiv 3 Aug 2025.
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36 of 67 references.
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