# Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging

arXiv: https://arxiv.org/abs/2009.04525 · HTML: https://mlsanity.com/paper/2009.04525/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2020.

## Built on by (most cited first, 30 of 40)

- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
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- [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)
- [Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network](https://mlsanity.com/paper/2108.11985/) (2021)
- [A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method](https://mlsanity.com/paper/2206.13103/) (2022)
- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Variational Physics Informed Neural Networks: the role of quadratures and test functions](https://mlsanity.com/paper/2109.02035/) (2021)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [Hybrid thermal modeling of additive manufacturing processes using physics-informed neural networks for temperature prediction and parameter identification](https://mlsanity.com/paper/2206.07756/) (2022)
- [Calibrating constitutive models with full-field data via physics informed neural networks](https://mlsanity.com/paper/2203.16577/) (2022)
- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Physics-informed neural networks for modeling rate- and temperature-dependent plasticity](https://mlsanity.com/paper/2201.08363/) (2022)
- [Spiking neural networks for nonlinear regression](https://mlsanity.com/paper/2210.03515/) (2022)
- [Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification](https://mlsanity.com/paper/2301.07609/) (2023)
- [EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials](https://mlsanity.com/paper/2410.10897/) (2024)
- [A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes](https://mlsanity.com/paper/2305.03184/) (2023)
- [MyCrunchGPT: A chatGPT assisted framework for scientific machine learning](https://mlsanity.com/paper/2306.15551/) (2023)
- [PhySRNet: Physics informed super-resolution network for application in computational solid mechanics](https://mlsanity.com/paper/2206.15457/) (2022)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [Dynamic fracture of a bicontinuously nanostructured copolymer: A deep-learning analysis of big-data-generating experiment](https://mlsanity.com/paper/2112.01971/) (2021)
- [G2Phinet: Relating Genotype and Biomechanical Phenotype of Tissues with Deep Learning](https://mlsanity.com/paper/2208.09889/) (2022)
- [Neural Control of Parametric Solutions for High-dimensional Evolution PDEs](https://mlsanity.com/paper/2302.00045/) (2023)
- [Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions](https://mlsanity.com/paper/2310.19590/) (2023)
- [Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Data](https://mlsanity.com/paper/2212.07723/) (2022)
- [Physics-Informed Machine Learning in Biomedical Science and Engineering](https://mlsanity.com/paper/2510.05433/) (2025)
- [Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials](https://mlsanity.com/paper/2306.01204/) (2023)

## Abstract (arXiv)

We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical properties of soft tissue based on the full-field displacement measurements under quasi-static loading. In our model, we apply two independent neural networks, one for approximating the solution of the corresponding forward problem, and the other for approximating the unknown material parameter field. As a proof of concept, we validate our model on a prototypical plane strain problem for incompressible hyperelastic tissue. The results show that the PINNs are effective in accurately recovering the unknown distribution of mechanical properties. By employing two neural networks in our model, we extend the capability of material identification of PINNs to include nonhomogeneous material parameter fields, which enables more flexibility of PINNs in representing complex material properties.