Design-space segmentation of an acoustic metamaterial for interpretability and insight

Acoustic metamaterials (AMMs) offer promising capabilities for noise control and wave manipulation, but their nonlinear and multidimensional design spaces often conceal clear relationships between geometry and acoustic performance. In this study, a data-driven methodology is proposed to segment the AMM design space into interpretable clusters based on spectral similarity, using unsupervised learning techniques. A large dataset of simulated absorptivity spectra, derived from systematic geometric parameter variations, is clustered using k-means, revealing distinct performance regimes. To enhance interpretability and physical insight, each cluster is characterized through representative spectral profiles and statistical analyses of its governing geometric features. Building on this segmentation, a surrogate classifier is trained to predict cluster membership from a given spectral response, enabling reverse mapping from performance targets to spectral classes. Additionally, a design implication matrix is introduced to provide interpretable guidelines that link desired acoustic performance with dominant geometric trends. To enable automatic geometry retrieval from the predicted cluster, a nearest-neighbor heuristic (NNH) is employed to return $m$ user-defined geometries corresponding to the target spectrum within the localized design subspace. This integrated framework facilitates targeted design exploration and offers a flexible, efficient, and interpretable alternative to conventional deep learning methods. It lays the groundwork for embedding interpretability into machine learning-assisted metamaterial design, thereby enabling actionable insights into anticipated system behavior.