  Metamaterials with functional responses, such as wave-based responses or
deformation-induced property variation under external stimuli, can exhibit
varying properties or functionalities under different conditions. Herein, we
aim at rapid inverse design of these metamaterials to meet target qualitative
functional behaviors. This inverse problem is challenging due to its
intractability and the existence of non-unique solutions. Past works mainly
focus on deep-learning-based methods that are data-demanding, require
time-consuming training and hyperparameter tuning, and are non-interpretable.
To overcome these limitations, we propose the Random-forest-based Interpretable
Generative Inverse Design (RIGID), an iteration-free, single-shot inverse
design method to achieve the fast generation of metamaterial designs with
on-demand functional behaviors. Unlike most existing methods, by exploiting the
interpretability of the random forest, we eliminate the need to train an
inverse model mapping responses to designs. Based on the likelihood of target
satisfaction derived from the trained forward model, one can sample design
solutions using Markov chain Monte Carlo methods. The RIGID method therefore
functions as a generative model that captures the conditional distribution of
satisfying solutions given a design target. We demonstrate the effectiveness
and efficiency of RIGID on both acoustic and optical metamaterial design
problems where only small datasets (less than 250 training samples) are
available. Synthetic design problems are created to further illustrate and
validate the mechanism of likelihood estimation in RIGID. This work offers a
new perspective on solving on-demand inverse design problems, showcasing the
potential for incorporating interpretable machine learning into generative
design and eliminating its large data requirement.
