Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data

📄 Abstract

Accurately estimating spatially heterogeneous elasticity parameters, particularly Young's modulus and Poisson's ratio, from noisy displacement measurements remains a significant challenge in inverse elasticity problems. Existing inverse estimation techniques are often limited by instability, high noise sensitivity, and difficulties in recovering the absolute scale of Young's modulus. This work presents a novel Inverse Elasticity Physics-Informed Neural Network (IE-PINN) to robustly reconstruct heterogeneous elasticity distributions from noisy displacement data based on the principles of linear elasticity. The IE-PINN incorporates three distinct neural network architectures, each dedicated to modeling displacement fields, strain fields, and elasticity distributions. This approach significantly enhances stability and accuracy under measurement noise. Additionally, a two-phase estimation strategy is proposed: the first phase recovers relative spatial distributions of Young's modulus and Poisson's ratio, while the second phase calibrates the absolute scale of Young's modulus using boundary loading conditions. Methodological innovations, including positional encoding, sine activation functions, and a sequential pretraining strategy, further improve the model's performance and robustness. Extensive numerical experiments demonstrate that IE-PINN effectively overcomes critical limitations faced by existing methods, providing accurate absolute-scale elasticity estimations even under severe noise conditions. This advancement holds substantial potential for clinical imaging diagnostics and mechanical characterization, where measurements typically encounter substantial noise.

📄 Installation

Clone the repository:

git clone https://github.com/data-science-tamu/IE-PINN.git
cd IE-PINN

Create and activate a Python environment (recommended):

python -m venv venv
source venv/bin/activate      # on Linux/Mac
venv\Scripts\activate         # on Windows

Install the required packages:

pip install -r requirements.txt

Run the code with the default configuration:

python main.py --config config.yaml

If you want to use a custom config file, pass the path:

python main.py --config path/to/your_config.yaml

📄 Data

The original datasets for simulation are from the published data in the work from :

C.-T. Chen, G. X. Gu
Learning hidden elasticity with deep neural networks
Proceedings of the National Academy of Sciences, 118 (31), Jul. 2021.
doi: 10.1073/pnas.2102721118

For this repository, noise is added before training with IE-PINN using the provided code.
Additional datasets with different boundary loading conditions are also included in the Datasets folder.

📄 Citation