Data-efficient Bayesian-guided design selection from large candidate sets: Application to hyperelastic stochastic metamaterials

TL;DR

This paper introduces a Bayesian-guided framework for efficiently selecting optimal designs from large candidate sets using limited high-fidelity evaluations, applicable to complex hyperelastic stochastic metamaterials.

Contribution

It develops a surrogate-based active learning approach that reduces the number of costly oracle evaluations needed for design selection in high-dimensional, unparameterized design spaces.

Findings

Active learning used less than 0.5% of candidates for training.

Achieved target accuracy with only a few oracle evaluations.

Effective in selecting optimal structures from 50,000 candidates.

Abstract

From a pool of admissible designs, we aim to identify a structure that achieves a target macroscopic stress response. For each candidate, the response is obtained from a high-fidelity oracle, such as expensive computational homogenization or experiments. We consider cases in which (i) the geometry cannot be conveniently parameterized, rendering gradient-based optimization inapplicable, and (ii) brute-force evaluation of all candidates is infeasible due to costly oracle queries. To tackle this challenge, we propose a Bayesian-guided design selection framework. The dimensionality of design variants is reduced through statistical feature engineering, and the resulting low-dimensional descriptors are mapped to effective hyperelastic constitutive parameters using a multi-output Gaussian process surrogate. The surrogate is trained using uncertainty-driven active learning with only a limited number of high-fidelity oracle evaluations. The surrogate shortlists promising candidates, and since its accuracy is inherently limited, the final selection of the optimal design is performed through high-fidelity oracle evaluations within the shortlist. In numerical test cases, we consider a design set of 50,000 candidate structures. Active learning requires labeling less than half a percent of the entire candidate set. Bayesian-guided design selection reaches a prescribed error threshold with only a handful of oracle evaluations in most cases.