# Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regression

arXiv: https://arxiv.org/abs/2605.31532 · HTML: https://mlsanity.com/paper/2605.31532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 18 of 18)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variables](https://mlsanity.com/paper/2401.14270/) (2024)
- [Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations](https://mlsanity.com/paper/2302.03598/) (2023)
- [Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticity](https://mlsanity.com/paper/2303.12164/) (2023)
- [Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)](https://mlsanity.com/paper/2503.05617/) (2025)
- [Automatic generation of interpretable hyperelastic material models by symbolic regression](https://mlsanity.com/paper/2206.15099/) (2022)
- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions](https://mlsanity.com/paper/2307.13149/) (2023)
- [Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2407.19326/) (2024)
- [Automated model discovery of finite strain elastoplasticity from uniaxial experiments](https://mlsanity.com/paper/2408.14615/) (2024)
- [Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models](https://mlsanity.com/paper/2602.17750/) (2026)
- [Physics-constrained symbolic model discovery for polyconvex incompressible hyperelastic materials](https://mlsanity.com/paper/2310.04286/) (2023)
- [A physics-augmented neural network framework for finite strain incompressible viscoelasticity](https://mlsanity.com/paper/2511.02959/) (2025)
- [Identification of Empirical Constitutive Models for Age-Hardenable Aluminium Alloy and High-Chromium Martensitic Steel Using Symbolic Regression](https://mlsanity.com/paper/2511.08424/) (2025)

## Abstract (arXiv)

Constitutive laws for inelastic materials must satisfy strict thermodynamic admissibility requirements, yet current data-driven approaches sacrifice interpretability, even when formal guarantees are provided by physics-encoded architectures. We propose a symbolic regression framework for the data-driven discovery of dissipation potentials governing the evolution of internal variables within the Generalized Standard Materials (GSM) formalism. Starting from the Clausius--Duhem inequality, we enforce the thermodynamic requirements, convexity and non-negativity, that the dual dissipation potential must satisfy to guarantee non-negative mechanical dissipation. These requirements are formulated in the general subdifferential setting, encompassing rate-dependent (viscoelastic) and viscoplastic dissipative mechanisms, including potentials with genuine elastic domains, within a unified framework. Candidate potentials are generated by a composition-extended convexity-preserving grammar that guarantees thermodynamic admissibility by construction. The framework is validated on synthetic datasets spanning Newtonian, power-law, and Bingham viscoplastic ground truths under process and measurement noise, and on experimental oscillatory shear measurements of a synthetic elastomer across multiple strain amplitudes and frequencies, where the discovered potentials reproduce the amplitude-dependent softening of the dynamic moduli and outperform a calibrated linear Zener baseline.