Unsupervised Constitutive Model Discovery from Sparse and Noisy Data

2025-10-15

AI Summary

Addressing the challenges of unsupervised constitutive model discovery from sparse, noisy experimental data—namely, poor physical consistency, weak identifiability, and difficulty in uncertainty quantification—this work proposes the first integration of statistical finite element modeling (statFEM) with the unsupervised constitutive learning framework EUCLID. The resulting joint inversion method simultaneously enforces mechanical equilibrium constraints, constitutive consistency, and probabilistic uncertainty modeling. By synergistically combining the virtual fields method, Bayesian inference, and unsupervised learning, it enables robust full-field displacement reconstruction and concurrent identification of constitutive relations. Validated on isotropic hyperelastic materials, the approach substantially reduces modeling errors induced by noise and data sparsity. It yields physically interpretable, probabilistically calibrated constitutive models with quantified confidence. This establishes a new paradigm for data-driven modeling of heterogeneous materials—one that jointly ensures accuracy, robustness, and interpretability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

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 or aim to yield interpretable constitutive models. In this work, we couple 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.

Problem

• Reducing sensitivity to noise and sparse data in model discovery
• Ensuring reconstructed fields comply with equilibrium and constitutive laws
• Coupling Bayesian field reconstruction with unsupervised constitutive model discovery

Innovation

• Couples statFEM with unsupervised constitutive model discovery
• Reduces sensitivity to noise and sparse data
• Ensures consistency with equilibrium and constitutive laws