Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures
Computational Physics
2025-08-11 v2 Machine Learning
Analysis of PDEs
Adaptation and Self-Organizing Systems
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.
Cite
@article{arxiv.2508.01854,
title = {Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures},
author = {Fanze Kong and Chen-Chih Lai and Yubin Lu},
journal= {arXiv preprint arXiv:2508.01854},
year = {2025}
}