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

arXiv: https://arxiv.org/abs/2603.15917 · HTML: https://mlsanity.com/paper/2603.15917/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 77 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [Unifying the design space and optimizing linear and nonlinear truss metamaterials by generative modeling](https://mlsanity.com/paper/2306.14773/) (2023)
- [Microstructure Generation via Generative Adversarial Network for Heterogeneous, Topologically Complex 3D Materials](https://mlsanity.com/paper/2006.13886/) (2020)
- [Microstructure reconstruction of 2D/3D random materials via diffusion-based deep generative models](https://mlsanity.com/paper/2311.17319/) (2023)
- [Differentiable graph-structured models for inverse design of lattice materials](https://mlsanity.com/paper/2304.05422/) (2023)
- [Inverse design of anisotropic microstructures using physics-augmented neural networks](https://mlsanity.com/paper/2412.13370/) (2024)
- [Deep learning-aided inverse design of porous metamaterials](https://mlsanity.com/paper/2507.17907/) (2025)
- [Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteria](https://mlsanity.com/paper/2509.16040/) (2025)
- [Unsupervised Constitutive Model Discovery from Sparse and Noisy Data](https://mlsanity.com/paper/2510.13559/) (2025)
- [On the Identifiability and Interpretability of Gaussian Process Models](https://mlsanity.com/paper/2310.17023/) (2023)
- [FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design](https://mlsanity.com/paper/2408.13532/) (2024)
- [Computational Design of Finite Strain Auxetic Metamaterials via Topology Optimization and Nonlinear Homogenization](https://mlsanity.com/paper/1905.00482/) (2019)
- [Reduced-order structure-property linkages for stochastic metamaterials](https://mlsanity.com/paper/2505.01283/) (2025)
- [Uncertainty quantification in model discovery by distilling interpretable material constitutive models from Gaussian process posteriors](https://mlsanity.com/paper/2510.22345/) (2025)

## Abstract (arXiv)

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.