Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning

TL;DR

This paper introduces RIGID, an interpretable, random-forest-based inverse design method for metamaterials that efficiently generates designs meeting target functional behaviors with limited training data.

Contribution

It presents a novel, single-shot inverse design approach using interpretable random forests and MCMC sampling, outperforming genetic algorithms in design space coverage.

Findings

RIGID successfully designs acoustic and optical metamaterials with fewer than 250 training samples.

It generates a broader range of solutions compared to genetic algorithms.

The method effectively incorporates interpretability into small-data inverse design tasks.

Abstract

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 "design$\rightarrow$response" forward model, eliminating the need for a more complex "response$\rightarrow$design" 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.