[2603.28707] A Convex Route to Thermomechanics: Learning Internal Energy and Dissipation

Computer Science > Computational Engineering, Finance, and Science arXiv:2603.28707 (cs) [Submitted on 30 Mar 2026] Title:A Convex Route to Thermomechanics: Learning Internal Energy and Dissipation Authors:Hagen Holthusen, Paul Steinmann, Ellen Kuhl View a PDF of the paper titled A Convex Route to Thermomechanics: Learning Internal Energy and Dissipation, by Hagen Holthusen and Paul Steinmann and Ellen Kuhl View PDF Abstract:We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a dissipation potential as primary constitutive functions, expressed in terms of deformation and entropy. This choice avoids the need to enforce mixed convexity--concavity conditions and facilitates a consistent incorporation of thermodynamic principles. In this contribution, we focus on materials without preferred directions or internal variables. While the formulation is posed in terms of entropy, the temperature is treated as the independent observable, and the entropy is inferred internally through the constitutive relation, enabling thermodynamically consistent modeling without requiring entropy data. Thermodynamic admissibility of the networks is guaranteed by construction. The internal energy and dissipation potential are represented by input convex neural networks, ensuring convexity and compliance with the second law. ...