Statistical-Physics-Informed Neural Networks (Stat-PINNs): A machine learning strategy for coarse-graining dissipative dynamics

Huang, Shenglin, Zequn, Zequn, Dirr, Nicolas ORCID: https://orcid.org/0000-0003-3634-7367, Zimmer, Johannes and Reina, Celia 2025. Statistical-Physics-Informed Neural Networks (Stat-PINNs): A machine learning strategy for coarse-graining dissipative dynamics. Journal of the Mechanics and Physics of Solids 194 , 105908. 10.1016/j.jmps.2024.105908 Item availability restricted.

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Abstract

Machine learning, with its remarkable ability for retrieving information and identifying patterns from data, has emerged as a powerful tool for discovering governing equations. It has been increasingly informed by physics, and more recently by thermodynamics, to further uncover the thermodynamic structure underlying the evolution equations, i.e., the thermodynamic potentials driving the system and the operators governing the kinetics. However, despite its great success, the inverse problem of thermodynamic model discovery from macroscopic data is in many cases non-unique, meaning that multiple pairs of potentials and operators can give rise to the same macroscopic dynamics, which significantly hinders the physical interpretability of the learned models. In this work, we propose a machine learning framework, named as Statistical-Physics-Informed Neural Networks (Stat-PINNs), which further encodes knowledge from statistical mechanics and resolves this non-uniqueness issue for the first time. The framework is here developed for purely dissipative isothermal systems. Interestingly, it only uses data from short-time particle simulations to learn the thermodynamic structure, which can in turn be used to predict long-time macroscopic evolutions. We demonstrate the approach for particle systems with Arrhenius-type interactions, common to a wide range of phenomena, such as defect diffusion in solids, surface absorption and chemical reactions. Our results from Stat-PINNs can successfully recover the known analytic solution for the case with long-range interactions and discover the hitherto unknown potential and operator governing the short-range interaction cases. We compare our results with an analogous approach that solely excludes statistical mechanics, and observe that, in addition to recovering the unique thermodynamic structure, statistical mechanics relations can increase the robustness and predictive capability of the learning strategy.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Elsevier
ISSN:	0022-5096
Date of First Compliant Deposit:	15 October 2024
Date of Acceptance:	13 October 2024
Last Modified:	26 Nov 2024 11:45
URI:	https://orca.cardiff.ac.uk/id/eprint/172890

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