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

TL;DR

This paper develops a Bayesian optimal experimental design framework to improve the reliability of learning history-dependent constitutive models, reducing experimental costs and enhancing parameter identifiability.

Contribution

It introduces practical approximations for efficient design optimization, enabling in silico experiments and improved physical testing strategies.

Findings

Optimized designs significantly improve parameter identifiability.

The framework reduces the number of experiments needed for reliable model calibration.

Numerical studies demonstrate enhanced learning of memory-related parameters.

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.