A Comparative Investigation of Thermodynamic Structure-Informed Neural Networks

TL;DR

This paper systematically compares various thermodynamic structure-informed neural networks, evaluating their accuracy, physical consistency, and robustness across different thermodynamic formulations and differential equations.

Contribution

It introduces a comprehensive comparison of thermodynamic formulations in neural networks, highlighting their impact on physical accuracy and robustness.

Findings

Newtonian-residual PINNs reconstruct states but lack thermodynamic quantity recovery

Structure-preserving formulations improve parameter identification and thermodynamic consistency

Results guide principled design of thermodynamics-consistent models

Abstract

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are incorporated. In this work, we present a systematic comparison of different thermodynamic structure-informed neural networks by incorporating various thermodynamics formulations, including Newtonian, Lagrangian, and Hamiltonian mechanics for conservative systems, as well as the Onsager variational principle and extended irreversible thermodynamics for dissipative systems. Through comprehensive numerical experiments on representative ordinary and partial differential equations, we quantitatively evaluate the impact of these formulations on accuracy, physical consistency, noise robustness, and interpretability. The results show that Newtonian-residual-based PINNs can reconstruct system states but fail to reliably recover key physical and thermodynamic quantities, whereas structure-preserving formulation significantly enhances parameter identification, thermodynamic consistency, and robustness. These findings provide practical guidance for principled design of thermodynamics-consistency model, and lay the groundwork for integrating more general nonequilibrium thermodynamic structures into physics-informed machine learning.