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), a 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.

通过随机森林的可解释性，提出了一种单次逆设计方法 RIGID，用于快速生成具有所需功能行为的变形材料设计。该方法不需要训练映射关系的逆模型，而是通过马尔科夫链蒙特卡洛方法从训练的前向模型导出目标满足的设计解决方案的条件分布。在仅有少量数据的情况下，RIGID 在声学和光学变形材料设计问题上展示了其效率和有效性，并进一步验证了其似然估计的机制，突显在生成设计和消除大数据需求方面，可解释机器学习的潜力。