# Generalized invariants meet constitutive neural networks: A novel framework for hyperelastic materials

arXiv: https://arxiv.org/abs/2508.12063 · HTML: https://mlsanity.com/paper/2508.12063/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 16 Aug 2025.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023)
- [On sparse regression, Lp-regularization, and automated model discovery](https://mlsanity.com/paper/2310.06872/) (2023)
- [Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID](https://mlsanity.com/paper/2305.16362/) (2023)
- [Polyconvex Physics-Augmented Neural Network Constitutive Models in Principal Stretches](https://mlsanity.com/paper/2503.00575/) (2025)
- [Material Fingerprinting: A shortcut to material model discovery without solving optimization problems](https://mlsanity.com/paper/2508.07831/) (2025)

## Built on by (most cited first, 3 of 3)

- [A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains](https://mlsanity.com/paper/2510.04187/) (2025)
- [CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data](https://mlsanity.com/paper/2606.14565/) (2026)
- [Benchmarking data-driven material models on the classic Treloar dataset](https://mlsanity.com/paper/2608.14063/) (2026)

## Abstract (arXiv)

The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven framework that simultaneously discovers appropriate invariants and constitutive models for isotropic incompressible hyperelastic materials. Our approach identifies both the most suitable invariants in a class of generalized invariants and the corresponding strain energy function directly from experimental observations. Unlike previous methods that rely on fixed invariant choices or sequential fitting procedures, our method integrates the discovery process into a single neural network architecture. By looking at a continuous family of possible invariants, the model can flexibly adapt to different material behaviors. We demonstrate the effectiveness of this approach using popular benchmark datasets for rubber and brain tissue. For rubber, the method recovers a stretch-dominated formulation consistent with classical models. For brain tissue, it identifies a formulation sensitive to small stretches, capturing the nonlinear shear response characteristic of soft biological matter. Compared to traditional and neural-network-based models, our framework provides improved predictive accuracy and interpretability across a wide range of deformation states. This unified strategy offers a robust tool for automated and physically meaningful model discovery in hyperelasticity.