Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures

Fanze Kong; Chen-Chih Lai; Yubin Lu

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arXiv · 2508.01854

Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures

Fanze Kong·Chen-Chih Lai·Yubin Lu

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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.

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physics.comp-ph cs.LG math.AP nlin.AO

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Fanze Kong, Chen-Chih Lai, Yubin Lu. 2025-08-03. Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures. https://arxiv.org/abs/2508.01854

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