# Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical Models

arXiv: https://arxiv.org/abs/2312.09787 · HTML: https://mlsanity.com/paper/2312.09787/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 75 references that are in the map.
- First posted on arXiv 15 Dec 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Correcting model misspecification in physics-informed neural networks (PINNs)](https://mlsanity.com/paper/2310.10776/) (2023)
- [Delta-PINNs: physics-informed neural networks on complex geometries](https://mlsanity.com/paper/2209.03984/) (2022)
- [Investigating molecular transport in the human brain from MRI with physics-informed neural networks](https://mlsanity.com/paper/2205.02592/) (2022)
- [Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps](https://mlsanity.com/paper/2201.12362/) (2022)
- [Ensemble learning for Physics Informed Neural Networks: a Gradient Boosting approach](https://mlsanity.com/paper/2302.13143/) (2023)
- [Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks](https://mlsanity.com/paper/2102.10863/) (2021)
- [Advanced discretization techniques for hyperelastic physics-augmented neural networks](https://mlsanity.com/paper/2306.09866/) (2023)

## Built on by (most cited first, 11 of 11)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [Simulating Three-dimensional Turbulence with Physics-informed Neural Networks](https://mlsanity.com/paper/2507.08972/) (2025)
- [Physics-Regularized Multi-Modal Image Assimilation for Brain Tumor Localization](https://mlsanity.com/paper/2409.20409/) (2024)
- [Physics-Informed Machine Learning in Biomedical Science and Engineering](https://mlsanity.com/paper/2510.05433/) (2025)
- [Enforcing hidden physics in physics-informed neural networks](https://mlsanity.com/paper/2511.14348/) (2025)
- [Physics-informed neural network estimation of active material properties in time-dependent cardiac biomechanical models](https://mlsanity.com/paper/2505.03382/) (2025)
- [Enhanced uncertainty quantification variational autoencoders for the solution of Bayesian inverse problems](https://mlsanity.com/paper/2502.13105/) (2025)
- [Non-Intrusive Parametrized-Background Data-Weak Reconstruction of Cardiac Displacement Fields from Sparse MRI-like Observations](https://mlsanity.com/paper/2509.14844/) (2025)
- [Non-Invasive Reconstruction of Cardiac Activation Dynamics Using Physics-Informed Neural Networks](https://mlsanity.com/paper/2603.03832/) (2026)
- [Where Physics Meets Privacy: Federated PINNs for Privacy-Preserving Brain Tumor Biomechanical Modeling](https://mlsanity.com/paper/2607.26207/) (2026)

## Abstract (arXiv)

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method and its great potential to enable the robust and effective identification of patient-specific, heterogeneous physical properties, s.a. tissue stiffness properties. In particular, we demonstrate the capability of the PINN to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.