A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling

TL;DR

This paper compares various thermodynamically consistent inelastic material modeling frameworks using neural networks, analyzing how their structural assumptions affect learning performance across different material datasets.

Contribution

It provides a unified neural network-based comparison of multiple thermodynamic modeling frameworks, highlighting how theoretical assumptions influence predictive capabilities.

Findings

Structural assumptions impact model learnability and generalization.

Convexity and duality restrictions affect stability and expressiveness.

Unified neural architecture isolates thermodynamic effects on performance.

Abstract

Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic framework and embed structural assumptions such as normality, dual dissipation potentials, or other structure from manually constructed models directly into the learning architecture. Consequently, differences in predictive performance may arise not only from data or network design, but also from the underlying theoretical assumptions. In this work, we present a unified comparison of several thermodynamically consistent inelastic modeling frameworks from a machine learning perspective. We consider internal-variable formulations with dissipation potential, generalized standard materials, and metriplectic structures, and we analyze their structural assumptions, admissible dependencies, convexity requirements, and implications for dissipation and evolution. Each framework is implemented within a common neural potential architecture based on invariant representations and neural ordinary differential equations. This unified setting ensures that performance differences can be attributed to thermodynamic structure rather than architectural variation. The models are trained and evaluated on three representative inelastic datasets generated from high-fidelity representative volume element simulations: an elastoplastic alloy, a viscoelastic composite, and a rate-dependent crystal plasticity polycrystal. By isolating the role of thermodynamic structure, we assess how restrictions such as duality, normality, operator-based evolution, and convexity influence learnability, expressiveness, stability, and generalization.