# Multi-fidelity Bayesian Data-Driven Design of Energy Absorbing Spinodoid Cellular Structures

arXiv: https://arxiv.org/abs/2507.22079 · HTML: https://mlsanity.com/paper/2507.22079/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 74 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [An Efficient Multi-fidelity Bayesian Optimization Approach for Analog Circuit Synthesis](https://mlsanity.com/paper/1912.00392/) (2019)
- [Leveraging Trust for Joint Multi-Objective and Multi-Fidelity Optimization](https://mlsanity.com/paper/2112.13901/) (2021)
- [Spiderweb nanomechanical resonators via Bayesian optimization: inspired by nature and guided by machine learning](https://mlsanity.com/paper/2108.04809/) (2021)
- [Multi-objective Bayesian Optimisation of Spinodoid Cellular Structures for Crush Energy Absorption](https://mlsanity.com/paper/2411.14508/) (2024)
- [Inverse designing surface curvatures by deep learning](https://mlsanity.com/paper/2309.00163/) (2023)

## Built on by (most cited first, 1 of 1)

- [Aligning Reasoning LLMs for Materials Discovery with Physics-aware Rejection Sampling](https://mlsanity.com/paper/2509.00768/) (2025)

## Abstract (arXiv)

Finite element (FE) simulations of structures and materials are getting increasingly more accurate, but also more computationally expensive as a collateral result. This development happens in parallel with a growing demand of data-driven design. To reconcile the two, a robust and data-efficient optimization method called Bayesian optimization (BO) has been previously established as a technique to optimize expensive objective functions. In parallel, the mesh width of an FE model can be exploited to evaluate an objective at a lower or higher fidelity (cost & accuracy) level. The multi-fidelity setting applied to BO, called multi-fidelity BO (MFBO), has also seen previous success. However, BO and MFBO have not seen a direct comparison with when faced with with a real-life engineering problem, such as metamaterial design for deformation and absorption qualities. Moreover, sampling quality and assessing design parameter sensitivity is often an underrepresented part of data-driven design. This paper aims to address these shortcomings by employing Sobol' samples with variance-based sensitivity analysis in order to reduce design problem complexity. Furthermore, this work describes, implements, applies and compares the performance BO with that MFBO when maximizing the energy absorption (EA) problem of spinodoid cellular structures is concerned. The findings show that MFBO is an effective way to maximize the EA of a spinodoid structure and is able to outperform BO by up to 11% across various hyperparameter settings. The results, which are made open-source, serve to support the utility of multi-fidelity techniques across expensive data-driven design problems.