Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data

2026-07-16 · Source: Machine Learning · Field: Science & Research — Engineering & Applied Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework is proposed to robustly estimate heterogeneous elastic properties, specifically Young's modulus and Poisson's ratio. This framework addresses the severely ill-posed inverse elasticity problem arising from low-resolution and noisy displacement data, a limitation for existing inverse methods. PIE-PINN models displacement observation, strain-discrepancy, and equilibrium residuals using Laplace distributions within a unified probabilistic model. To enhance robustness, it integrates a B-spline-guided displacement network for smooth global representation with a neural network correction for local variations. Furthermore, a hierarchical half-Cauchy model for displacement residual scales adaptively downweights severe fitting errors, improving the recovery of the latent mean displacement field. An alternating maximum-likelihood training strategy updates the mean and adjusts loss weights. Systematic case studies demonstrate PIE-PINN's robustness across varying noise levels and observation resolutions.

Key takeaway

For research scientists developing inverse elasticity models, PIE-PINN offers a robust approach to overcome challenges with low-resolution and noisy displacement data. You should consider integrating probabilistic modeling with adaptive error weighting and hybrid network architectures, like B-spline guidance, to improve the accuracy and stability of your material property estimations. This framework can significantly enhance the reliability of inverse problem solutions in real-world scenarios where high-fidelity data is scarce.

Key insights

PIE-PINN robustly estimates heterogeneous elastic properties from noisy, low-resolution data using a probabilistic physics-informed neural network with B-spline guidance.

Principles

• Probabilistic modeling enhances robustness in ill-posed inverse problems.
• Combining global smooth representations with local corrections improves field recovery.
• Adaptive weighting of errors mitigates noise sensitivity.

Method

PIE-PINN models residuals with Laplace distributions, combining a B-spline-guided displacement network and a hierarchical half-Cauchy model for residual scales. An alternating maximum-likelihood strategy updates mean and adjusts loss weights.

In practice

• Apply B-spline guidance for smooth global field representation.
• Use hierarchical scale models to downweight severe fitting errors.
• Employ alternating maximum-likelihood for robust training.

Topics

• Physics-Informed Neural Networks
• Inverse Elasticity
• Probabilistic Modeling
• Heterogeneous Materials
• B-spline Networks

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.