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.

翻译：具有功能响应的超材料，例如基于波的响应或在外部刺激下由变形引起的性能变化，能够在不同条件下展现出变化的特性或功能。本文旨在快速逆向设计此类超材料，以满足目标定性功能行为。由于该逆向问题的难解性及解的非唯一性，这一任务极具挑战性。以往的研究主要集中于基于深度学习的方法，这些方法数据需求大、需要耗时的训练和超参数调整，且缺乏可解释性。为克服这些局限，我们提出了基于随机森林的可解释生成式逆向设计方法，这是一种无需迭代、单步完成的逆向设计方法，能够快速生成具有按需功能行为的超材料设计。与大多数现有方法不同，通过利用随机森林的可解释性，我们无需训练一个从响应到设计的逆向映射模型。基于从已训练的正向模型中推导出的目标满足似然度，可以使用马尔可夫链蒙特卡洛方法对设计方案进行采样。因此，RIGID方法作为一种生成模型，能够捕捉在给定设计目标下满足条件的解的条件分布。我们在仅有小规模数据集（少于250个训练样本）可用的声学和光学超材料设计问题上验证了RIGID方法的有效性和效率。创建了合成设计问题以进一步说明和验证RIGID中似然估计的机制。这项工作为解决按需逆向设计问题提供了新的视角，展示了将可解释机器学习融入生成式设计并消除其大数据需求的潜力。