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

Area of Science:

• Computational Mechanics
• Applied Physics
• Machine Learning

Background:

• Estimating heterogeneous elasticity parameters (Young's modulus, Poisson's ratio) from noisy displacement data is challenging in inverse elasticity problems.
• Current methods suffer from instability, noise sensitivity, and difficulty in determining the absolute scale of Young's modulus.

Purpose of the Study:

• To develop a robust method for reconstructing spatially heterogeneous elasticity distributions from noisy displacement measurements.
• To overcome the limitations of existing inverse estimation techniques, particularly in handling noise and determining absolute material properties.

Main Methods:

• A novel Inverse Elasticity Physics-Informed Neural Network (IE-PINN) was developed, integrating three neural networks for displacement, strain, and elasticity fields.
• A two-phase estimation strategy was employed: relative distribution recovery followed by absolute scale calibration using boundary conditions.
• Methodological innovations include positional encoding, sine activation functions, and sequential pretraining for enhanced performance and robustness.

Main Results:

• The IE-PINN demonstrated robust reconstruction of heterogeneous elasticity distributions even with significant measurement noise.
• The two-phase strategy successfully recovered both relative spatial distributions and the absolute scale of Young's modulus.
• The proposed method significantly outperforms existing techniques in accuracy and stability under noisy conditions.

Conclusions:

• The IE-PINN provides an accurate and stable solution for estimating absolute-scale elasticity parameters from noisy displacement data.
• This advancement has significant implications for applications like clinical imaging diagnostics and mechanical characterization where noise is prevalent.