# How to See Hidden Patterns in Metamaterials with Interpretable Machine Learning

arXiv: https://arxiv.org/abs/2111.05949 · HTML: https://mlsanity.com/paper/2111.05949/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 75 references that are in the map.
- First posted on arXiv 10 Nov 2021.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [The Bayesian Case Model: A Generative Approach for Case-Based Reasoning and Prototype Classification](https://mlsanity.com/paper/1503.01161/) (2015)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [A Generative Model for Inverse Design of Metamaterials](https://mlsanity.com/paper/1805.10181/) (2018)

## Built on by (most cited first, 5 of 5)

- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning](https://mlsanity.com/paper/2401.00003/) (2023)
- [Harnessing Interpretable Machine Learning for Holistic Inverse Design of Origami](https://mlsanity.com/paper/2204.07235/) (2022)
- [Phononic materials with effectively scale-separated hierarchical features using interpretable machine learning](https://mlsanity.com/paper/2408.08428/) (2024)
- [Learning Metamaterial Eigenmodes with Wavelet-Encoded Fourier Neural Operators](https://mlsanity.com/paper/2609.08102/) (2026)

## Abstract (arXiv)

Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning processes are opaque and require enormous datasets that are expensive to obtain. In this work, we develop two novel machine learning approaches to metamaterials discovery that have neither of these disadvantages. These approaches, called shape-frequency features and unit-cell templates, can discover 2D metamaterials with user-specified frequency band gaps. Our approaches provide logical rule-based conditions on metamaterial unit-cells that allow for interpretable reasoning processes, and generalize well across design spaces of different resolutions. The templates also provide design flexibility where users can almost freely design the fine resolution features of a unit-cell without affecting the user's desired band gap.