PIE-PINN Estimates Elastic Properties from Noisy, Low-Res Data

This research addresses the challenging inverse elasticity problem of estimating spatially varying elastic properties from limited and imperfect displacement measurements. Traditional methods often struggle with low-resolution data and noise, which can amplify errors during inverse estimation. The proposed solution is PIE-PINN, a Probabilistic Inverse Elasticity Physics-Informed Neural Network framework. PIE-PINN enhances robustness by modeling various residuals (displacement observation, strain-discrepancy, equilibrium) using Laplace distributions within a unified probabilistic model. It integrates a B-spline-guided displacement network for smooth global representation with a neural network for local variations, and a hierarchical half-Cauchy model to adaptively downweight severe displacement fitting errors. An alternating maximum-likelihood training strategy further refines the estimation. Case studies confirm PIE-PINN's robustness across different noise levels and resolutions, particularly for Young's modulus and Poisson's ratio estimation.