Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws

2026-03-12

AI Summary

This study addresses the challenge of unreliable parameter identification in history-dependent constitutive models under limited experimental budgets, where insufficient data often compromises inference accuracy—particularly for parameters governing memory effects. To enhance identifiability, the authors propose an efficient framework based on Bayesian optimal experimental design that optimizes experimental protocols by maximizing expected information gain. To mitigate computational costs, a surrogate model is constructed using Gaussian approximations and the Fisher information matrix, enabling rapid optimization of batch experimental designs for complex material testing. Demonstrated on uniaxial tests of viscoelastic solids, the optimized specimen geometries and loading paths significantly outperform random designs, markedly reducing the number of required physical experiments while improving the precision of parameter estimates.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Bayesian Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to quantify, interpret, and maximize the utility of experimental designs for reliable learning of history-dependent constitutive models. In this framework, the design utility is defined as the expected reduction in parametric uncertainty or the expected information gain. This enables in silico design optimization using simulated data and reduces the cost of physical experiments for reliable parameter identification. We introduce two approximations that make this framework practical for advanced material testing with expensive forward models and high-dimensional data: (i) a Gaussian approximation of the expected information gain, and (ii) a surrogate approximation of the Fisher information matrix. The former enables efficient design optimization and interpretation, while the latter extends this approach to batched design optimization by amortizing the cost of repeated utility evaluations. Our numerical studies of uniaxial tests for viscoelastic solids show that optimized specimen geometries and loading paths yield image and force data that significantly improve parameter identifiability relative to random designs, especially for parameters associated with memory effects.

Problem

• history-dependent constitutive laws
• parameter identifiability
• optimal experimental design
• parametric uncertainty
• experimental budget

Innovation

• Bayesian optimal experimental design
• history-dependent constitutive laws
• expected information gain
• surrogate approximation
• parameter identifiability