Statistical-Physics-Informed Neural Networks (Stat-PINNs) - A Machine Learning Strategy for Coarse-graining Dissipative Dynamics

Aug 5, 2026

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Machine learning can infer governing equations from data, but thermodynamic model discovery from macroscopic behavior is often non-unique, limiting physical interpretability. Statistical-Physics-Informed Neural Networks (Stat-PINNs) encode statistical-mechanics knowledge to resolve this nonuniqueness for purely dissipative isothermal systems. Using only short-time particle simulation data, the method learns thermodynamic structure and predicts long-time macroscopic evolution. Tests on Arrhenius-type interactions recover known analytic results and discover new potentials and operators, with robustness gains from thermodynamic constraints.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages23

Reading Time58 min

AccessFree to download

Introduction

Dissipative phenomena and modeling challenges

GENERIC thermodynamic structure

Method framework and key idea

Statistical-physics-informed learning

Nonuniqueness resolution from macroscopic data

Applications and validation

Short-time particle simulations and long-time prediction

Arrhenius-type interactions

Comparisons and robustness effects

ORCA – Online Research @ Cardiff This is an Open Access document downloaded from ORCA, Cardiff University's institutional repository:[https://orca.cardiff.ac.uk/id/eprint/172890/](https://orca.cardiff.ac.uk/id/eprint/172890/) This is the author’s version of a work that was submitted to / accepted for publication. Citation for final published version: Huang, Shenglin, Zequn, Zequn, Dirr, Nicolas , Zimmer, Johannes and Reina, Celia 2025. StatisticalPhysics-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 Publishers page: [https://doi.org/10.1016/j.jmps.2024.105908](https://doi.org/10.1016/j.jmps.2024.105908) Please note: Changes made as a result of publishing processes such as copy-editing, formatting and page numbers may not be reflected in this version. For the definitive version of this publication, please refer to the published source. You are advised to consult the publisher’s version if you wish to cite this paper. This version is being made available in accordance with publisher policies. See [http://orca.cf.ac.uk/policies.html](http://orca.cf.ac.uk/policies.html) for usage policies. Copyright and moral rights for publications made available in ORCA are retained by the copyright holders. Statistical-Physics-Informed Neural Networks (Stat-PINNs): A Machine Learning Strategy for Coarse-graining Dissipative Dynamics Shenglin Huang 1 , Zequn He 1 , Nicolas Dirr2 , Johannes Zimmer3 , and Celia Reina 1 ∗ 1 Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA 2 School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK and 3 School of Computation, Information and Technology, Technische Universität München, Boltzmannstr. 3, 85748 Garching, Germany 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 nonuniqueness 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. I. INTRODUCTION Dissipative phenomena are pervasive across material systems, from diffusion in gases,

FAQs

What problem does Stat-PINNs address in thermodynamic model discovery?

It addresses the nonuniqueness issue where multiple thermodynamic potentials and operators can produce the same macroscopic dynamics, reducing physical interpretability.

What input data does Stat-PINNs require to learn the thermodynamic structure?

It uses only data from short-time particle simulations to learn the thermodynamic structure.

How does Stat-PINNs perform on dissipative systems with Arrhenius-type interactions?

It recovers the known analytic solution for long-range interactions and discovers previously unknown potentials and operators for short-range interaction cases, and improves robustness versus approaches excluding statistical mechanics.

Aug 5, 2026

Upload by Noah