# Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning

arXiv: https://arxiv.org/abs/2401.00003 · HTML: https://mlsanity.com/paper/2401.00003/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 105 references that are in the map.
- First posted on arXiv 8 Dec 2023.

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

- [Synthesizing Tabular Data using Generative Adversarial Networks](https://mlsanity.com/paper/1811.11264/) (2018)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [VAEM: a Deep Generative Model for Heterogeneous Mixed Type Data](https://mlsanity.com/paper/2006.11941/) (2020)
- [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)
- [Inverse-design of nonlinear mechanical metamaterials via video denoising diffusion models](https://mlsanity.com/paper/2305.19836/) (2023)
- [A Generative Model for Inverse Design of Metamaterials](https://mlsanity.com/paper/1805.10181/) (2018)
- [Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties](https://mlsanity.com/paper/2302.12881/) (2023)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Designing nanophotonic structures using conditional-deep convolutional generative adversarial networks](https://mlsanity.com/paper/1903.08432/) (2019)
- [METASET: Exploring Shape and Property Spaces for Data-Driven Metamaterials Design](https://mlsanity.com/paper/2006.02142/) (2020)
- [Multifunctional Metasurface Design with a Generative Adversarial Network](https://mlsanity.com/paper/1908.04851/) (2019)
- [Freeform Diffractive Metagrating Design Based on Generative Adversarial Networks](https://mlsanity.com/paper/1811.12436/) (2018)
- [GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty](https://mlsanity.com/paper/2202.10558/) (2022)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [Diffusion Probabilistic Model Based Accurate and High-Degree-of-Freedom Metasurface Inverse Design](https://mlsanity.com/paper/2304.13038/) (2023)
- [How to See Hidden Patterns in Metamaterials with Interpretable Machine Learning](https://mlsanity.com/paper/2111.05949/) (2021)
- [Deep Neural Operator Enabled Concurrent Multitask Design for Multifunctional Metamaterials under Heterogeneous Fields](https://mlsanity.com/paper/2312.02403/) (2023)

## Built on by (most cited first, 3 of 3)

- [Inverse design of Non-parameterized Ventilated Acoustic Resonator via Variational Autoencoder with Acoustic Response-encoded Latent Space](https://mlsanity.com/paper/2408.05917/) (2024)
- [RAG: A Random-Forest-Based Generative Design Framework for Uncertainty-Aware Design of Metamaterials with Complex Functional Response Requirements](https://mlsanity.com/paper/2601.13233/) (2026)
- [Reinforcement learning for inverse silhouette design and rapid laser cutting of compact parallelogram quad kirigami prototypes](https://mlsanity.com/paper/2605.08098/) (2026)

## Abstract (arXiv)

Metamaterials with functional responses can exhibit varying properties under different conditions (e.g., wave-based responses or deformation-induced property variation). This work addresses the rapid inverse design of such metamaterials to meet target qualitative functional behaviors, a challenge due to its intractability and non-unique solutions. Unlike data-intensive and non-interpretable deep-learning-based methods, we propose the Random-forest-based Interpretable Generative Inverse Design (RIGID), a single-shot inverse design method for fast generation of metamaterial designs with on-demand functional behaviors. RIGID leverages the interpretability of a random forest-based "designrightarrowresponse" forward model, eliminating the need for a more complex "responserightarrowdesign" inverse model. Based on the likelihood of target satisfaction derived from the trained random forest, one can sample a desired number of design solutions using Markov chain Monte Carlo methods. We validate RIGID on acoustic and optical metamaterial design problems, each with fewer than 250 training samples. Compared to the genetic algorithm-based design generation approach, RIGID generates satisfactory solutions that cover a broader range of the design space, allowing for better consideration of additional figures of merit beyond target satisfaction. This work offers a new perspective on solving on-demand inverse design problems, showcasing the potential for incorporating interpretable machine learning into generative design under small data constraints.