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

2025-06-16

AI Summary

Inverse elasticity problems face persistent challenges—including solution instability, loss of absolute scale, and noise sensitivity—when estimating spatially heterogeneous Young’s modulus and Poisson’s ratio from noisy displacement data. To address these, we propose a tri-network collaborative inverse elasticity physics-informed neural network (IE-PINN). Our method introduces a novel three-branch architecture that explicitly decouples displacement, strain, and elastic parameter fields; employs a two-stage strategy—first learning relative spatial distributions, then enforcing physical constraints to recover the absolute scale of Young’s modulus; and integrates positional encoding, Sine activation, and sequential pretraining to enhance robustness against measurement noise. Experiments demonstrate that IE-PINN achieves high-fidelity, physically consistent reconstruction of heterogeneous elastic parameters even under severe noise, substantially outperforming conventional inversion methods. This work establishes a new, interpretable, and generalizable paradigm for clinical elastography and nondestructive material characterization.

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Abstract

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.

Problem

• Estimating heterogeneous elasticity parameters from noisy data
• Overcoming instability and noise sensitivity in inverse elasticity
• Recovering absolute-scale Young's modulus accurately

Innovation

• IE-PINN integrates three neural networks
• Two-phase strategy recovers elasticity parameters
• Uses positional encoding and sine activation