# Calibrating constitutive models with full-field data via physics informed neural networks

arXiv: https://arxiv.org/abs/2203.16577 · HTML: https://mlsanity.com/paper/2203.16577/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 59 references that are in the map.
- First posted on arXiv 30 Mar 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks](https://mlsanity.com/paper/2104.08426/) (2021)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Physics informed deep learning for computational elastodynamics without labeled data](https://mlsanity.com/paper/2006.08472/) (2020)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging](https://mlsanity.com/paper/2009.04525/) (2020)
- [Model-Free Data-Driven Inelasticity](https://mlsanity.com/paper/1808.10859/) (2018)
- [The mixed deep energy method for resolving concentration features in finite strain hyperelasticity](https://mlsanity.com/paper/2104.09623/) (2021)
- [Discovering plasticity models without stress data](https://mlsanity.com/paper/2202.04916/) (2022)
- [Meshless physics-informed deep learning method for three-dimensional solid mechanics](https://mlsanity.com/paper/2012.01547/) (2020)
- [Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks](https://mlsanity.com/paper/2105.00862/) (2021)
- [Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties](https://mlsanity.com/paper/2203.07422/) (2022)
- [Data-driven fracture mechanics](https://mlsanity.com/paper/2006.03133/) (2020)

## Built on by (most cited first, 12 of 12)

- [Modular machine learning-based elastoplasticity: generalization in the context of limited data](https://mlsanity.com/paper/2210.08343/) (2022)
- [Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Data](https://mlsanity.com/paper/2212.07723/) (2022)
- [Differentiable programming across the PDE and Machine Learning barrier](https://mlsanity.com/paper/2409.06085/) (2024)
- [Identifying Constitutive Parameters for Complex Hyperelastic Materials using Physics-Informed Neural Networks](https://mlsanity.com/paper/2308.15640/) (2023)
- [Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)](https://mlsanity.com/paper/2604.07746/) (2026)
- [Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks](https://mlsanity.com/paper/2405.18311/) (2024)
- [Compliance Minimization via Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2507.09968/) (2025)
- [Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables](https://mlsanity.com/paper/2308.03915/) (2023)
- [Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data](https://mlsanity.com/paper/2506.14036/) (2025)
- [Spectral-Bias and Kernel-Task Alignment in Physically Informed Neural Networks](https://mlsanity.com/paper/2307.06362/) (2023)
- [Should We Simultaneously Calibrate Multiple Computer Models?](https://mlsanity.com/paper/2505.18176/) (2025)
- [Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data](https://mlsanity.com/paper/2607.14563/) (2026)

## Abstract (arXiv)

The calibration of solid constitutive models with full-field experimental data is a long-standing challenge, especially in materials which undergo large deformation. In this paper, we propose a physics-informed deep-learning framework for the discovery of constitutive model parameterizations given full-field displacement data and global force-displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic materials models suitable for different material classes is considered including the Neo-Hookean, Gent, and Blatz-Ko constitutive models as exemplars for general hyperelastic behavior, polymer behavior with lock-up, and compressible foam behavior respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full-field experimental data is utilized to calibrate constitutive models under finite deformations.