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

arXiv: https://arxiv.org/abs/2506.14036 · HTML: https://mlsanity.com/paper/2506.14036/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 99 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [Automated discovery of generalized standard material models with EUCLID](https://mlsanity.com/paper/2211.04453/) (2022)
- [Discovering plasticity models without stress data](https://mlsanity.com/paper/2202.04916/) (2022)
- [Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks](https://mlsanity.com/paper/2308.12716/) (2023)
- [Calibrating constitutive models with full-field data via physics informed neural networks](https://mlsanity.com/paper/2203.16577/) (2022)
- [Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials](https://mlsanity.com/paper/2306.01204/) (2023)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data](https://mlsanity.com/paper/2607.14563/) (2026)

## Abstract (arXiv)

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.