# Unsupervised Constitutive Model Discovery from Sparse and Noisy Data

arXiv: https://arxiv.org/abs/2510.13559 · HTML: https://mlsanity.com/paper/2510.13559/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2025.

## Built on by (most cited first, 3 of 3)

- [Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models](https://mlsanity.com/paper/2602.17750/) (2026)
- [Data-efficient Bayesian-guided design selection from large candidate sets: Application to hyperelastic stochastic metamaterials](https://mlsanity.com/paper/2603.15917/) (2026)
- [Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data](https://mlsanity.com/paper/2606.05199/) (2026)

## Abstract (arXiv)

Recently, unsupervised constitutive model discovery has gained attention through frameworks based on the Virtual Fields Method (VFM), most prominently the EUCLID approach. However, the performance of VFM-based approaches, including EUCLID, is affected by measurement noise and data sparsity, which are unavoidable in practice. The statistical finite element method (statFEM) offers a complementary perspective by providing a Bayesian framework for assimilating noisy and sparse measurements to reconstruct the full-field displacement response, together with quantified uncertainty. While statFEM recovers displacement fields under uncertainty, it does not strictly enforce consistency with constitutive relations. In this work, we integrate statFEM with unsupervised constitutive model discovery in the EUCLID framework, yielding statFEM-EUCLID. The framework is demonstrated for isotropic hyperelastic materials. The results show that this integration reduces sensitivity to noise and data sparsity, while ensuring that the reconstructed fields remain consistent with both equilibrium and constitutive laws.