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

arXiv:2603.15917 · cs.CE, stat.ML · Submitted 2026-03-16 · Read on arXiv

cs.CE, stat.ML

Submitted: 2026-03-16

Updated: 2026-09-08

Code: https://github.com/hooman-danesh/BayGDS

License: http://creativecommons.org/licenses/by/4.0/

The gist: From a pool of admissible designs, we aim to identify a structure that achieves a target macroscopic stress response.

Terminology

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.

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