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Metamaterials with functional responses, such as wave-based responses ordeformation-induced property variation under external stimuli, can exhibitvarying properties or functionalities under different conditions. Herein, weaim at rapid inverse design of these metamaterials to meet target qualitativefunctional behaviors. This inverse problem is challenging due to itsintractability and the existence of non-unique solutions. Past works mainlyfocus on deep-learning-based methods that are data-demanding, requiretime-consuming training and hyperparameter tuning, and are non-interpretable.To overcome these limitations, we propose the Random-forest-based InterpretableGenerative Inverse Design (RIGID), a single-shot inverse design method toachieve the fast generation of metamaterial designs with on-demand functionalbehaviors. Unlike most existing methods, by exploiting the interpretability ofthe random forest, we eliminate the need to train an inverse model mappingresponses to designs. Based on the likelihood of target satisfaction derivedfrom the trained forward model, one can sample design solutions using Markovchain Monte Carlo methods. The RIGID method therefore functions as a generativemodel that captures the conditional distribution of satisfying solutions givena design target. We demonstrate the effectiveness and efficiency of RIGID onboth acoustic and optical metamaterial design problems where only smalldatasets (less than 250 training samples) are available. Synthetic designproblems are created to further illustrate and validate the mechanism oflikelihood estimation in RIGID. This work offers a new perspective on solvingon-demand inverse design problems, showcasing the potential for incorporatinginterpretable machine learning into generative design and eliminating its largedata requirement.

Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning