# Identifying Constitutive Parameters for Complex Hyperelastic Materials using Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2308.15640 · HTML: https://mlsanity.com/paper/2308.15640/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 89 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems](https://mlsanity.com/paper/2203.00003/) (2022)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging](https://mlsanity.com/paper/2009.04525/) (2020)
- [A Physics-Guided Neural Network Framework for Elastic Plates: Comparison of Governing Equations-Based and Energy-Based Approaches](https://mlsanity.com/paper/2010.06050/) (2020)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [Physics-Informed Neural Networks for Shell Structures](https://mlsanity.com/paper/2207.14291/) (2022)
- [Calibrating constitutive models with full-field data via physics informed neural networks](https://mlsanity.com/paper/2203.16577/) (2022)
- [Dynamic fracture of a bicontinuously nanostructured copolymer: A deep-learning analysis of big-data-generating experiment](https://mlsanity.com/paper/2112.01971/) (2021)
- [Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Data](https://mlsanity.com/paper/2212.07723/) (2022)

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

- [Finite-PINN: A Physics-Informed Neural Network with Finite Geometric Encoding for Solid Mechanics](https://mlsanity.com/paper/2412.09453/) (2024)
- [Physics-Informed Neural Network based Damage Identification for Truss Railroad Bridges](https://mlsanity.com/paper/2502.00194/) (2025)
- [A Research Prototype for Closed-Loop Generative Design of Customized Foot Orthoses via Semantic-Physics Alignment](https://mlsanity.com/paper/2607.16631/) (2026)

## Abstract (arXiv)

Identifying constitutive parameters in engineering and biological materials, particularly those with intricate geometries and mechanical behaviors, remains a longstanding challenge. The recent advent of Physics-Informed Neural Networks (PINNs) offers promising solutions, but current frameworks are often limited to basic constitutive laws and encounter practical constraints when combined with experimental data. In this paper, we introduce a robust PINN-based framework designed to identify material parameters for soft materials, specifically those exhibiting complex constitutive behaviors, under large deformation in plane stress conditions. Distinctively, our model emphasizes training PINNs with multi-modal synthetic experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even with noisy data. Our results reveal that the PINNs framework can accurately identify constitutive parameters of the incompressible Arruda-Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%. We believe our framework provides a robust modulus identification approach for complex solids, especially for those with geometrical and constitutive complexity.