Title: Learning Non-Gradient Diffusion Systems via Moment-Evolution and Energetic Variational Approaches
Primary area: learning on time series and dynamical systems
Keywords: Physics-informed machine learning; Non-gradient system; Energetic variational approach; Data-driven modeling

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 diffusions 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.

TL;DR: We propose a two-stage framework that learns pseudo-potentials and rotational components in non-gradient diffusions from data using moment estimates and energy dissipation laws.