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This paper introduces the Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework, which effectively estimates heterogeneous elastic properties like Young's modulus and Poisson's ratio from low-resolution, noisy displacement data. By integrating a B-spline-guided displacement network with a hierarchical half-Cauchy model, PIE-PINN enhances robustness against measurement noise and resolution degradation, addressing the challenges of traditional inverse methods that rely on high-fidelity observations. Systematic evaluations reveal that PIE-PINN significantly improves the recovery of latent displacement fields, outperforming existing techniques in various noise and resolution scenarios.
Robustly estimating elastic properties from low-resolution, noisy data is now feasible with the PIE-PINN framework, which adapts to measurement uncertainties like never before.
Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitting errors are amplified through inverse estimation. Existing inverse methods often rely on high-fidelity observations and manually prespecified loss weights, limiting their adaptability and making them sensitive to noise and resolution degradation. We propose a Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework for robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data. PIE-PINN models displacement observation, strain-discrepancy, and equilibrium residuals using Laplace distributions within a unified probabilistic model. To improve robustness, the framework combines a B-spline-guided displacement network with a hierarchical half-Cauchy model for displacement residual scales. The B-spline provides a smooth global representation of the displacement field, while the neural network correction captures local variations. The hierarchical scale model adaptively downweights severe displacement fitting errors, enabling more robust recovery of the latent mean displacement field. An alternating maximum-likelihood training strategy updates the mean through weighted residual minimization and updates the scales to adjust the loss weights. Systematic case studies across varying noise levels and observation resolutions demonstrate the robustness of PIE-PINN.
