Navigating Competing Constraints in Acoustic Metamaterials via Physically Admissible Design Spaces
Abstract
Achieving simultaneously high absorption, broad bandwidth, and minimal thickness remains a central challenge in sound‐absorbing metamaterials. Multilayered Helmholtz resonators (MLHR) offer a promising route, yet effective design under competing constraints remains nontrivial. Here, we present MLHR acoustic metamaterials that overcome competing constraints by navigating physically admissible design spaces enabled by a physics‐informed variational autoencoder. In this framework, the decoded geometries are evaluated using a differentiable analytical MLHR acoustic model, which enforces physical admissibility while maintaining direct coupling to the underlying acoustic principles. This architecture enables the learning of a compact, smooth, and physically structured latent space that captures relationships between geometry and absorption spectra. Building on this representation, Bayesian optimization is performed efficiently in latent space to realize targeted inverse designs under competing objectives, including high absorption coefficients, broad continuous bandwidth, and minimal sample thickness. Conceptual demonstration through 3D‐printed samples reveals excellent agreement between predicted and measured absorption responses. For instance, one optimized metamaterial with an ultralow thickness of 13.7 mm displays effective broadband absorption with an average absorption coefficient of 0.7 across a broad frequency range from 1000 to 6000 Hz. Overall, this work establishes a versatile and physically grounded platform for the rational design of MLHR‐based acoustic metamaterials.