Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Data
This work addresses a critical problem in clinical imaging diagnostics and mechanical characterization, where measurements are often noisy, though it appears incremental as it builds on existing physics-informed neural network approaches.
The paper tackles the challenge of estimating spatially heterogeneous elasticity parameters from noisy displacement data by introducing an Inverse Elasticity Physics-Informed Neural Network (IE-PINN), which achieves accurate absolute-scale estimations even under severe noise conditions.
Accurately estimating spatially heterogeneous elasticity parameters, particularly Young's modulus and Poisson's ratio, from noisy displacement measurements remains significantly challenging in inverse elasticity problems. Existing inverse estimation techniques are often limited by instability, pronounced sensitivity to measurement noise, and difficulty in recovering absolute-scale Young's modulus. This work presents a novel Inverse Elasticity Physics-Informed Neural Network (IE-PINN) specifically designed to robustly reconstruct heterogeneous distributions of elasticity parameters from noisy displacement data based on linear elasticity physics. IE-PINN integrates three distinct neural network architectures dedicated to separately modeling displacement fields, strain fields, and elasticity distributions, thereby significantly enhancing stability and accuracy against measurement noise. Additionally, a two-phase estimation strategy is introduced: the first phase recovers relative spatial distributions of Young's modulus and Poisson's ratio, and the second phase calibrates the absolute scale of Young's modulus using imposed loading boundary conditions. Additional methodological innovations, including positional encoding, sine activation functions, and a sequential pretraining protocol, further enhance the model's performance and robustness. Extensive numerical experiments demonstrate that IE-PINN effectively overcomes critical limitations encountered by existing methods, delivering 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.