Machine learning-assisted broadband sound focusing based on integrated-resonant meta-atoms

In modern acoustic engineering, metamaterials-based focusing technology enables precise control of sound waves, expanding applications such as acoustic imaging and nondestructive testing. However, traditional acoustic metamaterials suffer from narrow bandwidth due to strong dispersion induced by their inherent localized resonance. Here, we numerically and experimentally demonstrate a machine learning-assisted broadband achromatic acoustic focusing metalens (BAAFM), composed of 40 integrated-resonant meta-atoms (IRMs) engineered via a Gaussian Bayesian-based Entropy Search Portfolio (GB-ESP) framework. The BAAFM realizes broadband achromatic operation through each unit's linear phase shift (phase agreement exceeding 93%) enabled by the occurrence of the integrated-resonant state. By synergizing exploration-exploitation-balanced ESP guided GB inference, the optimization framework efficiently tackles the high-dimensional (40×6 parameters) complexity, ensuring robust convergence only within 100 iterations per IRM. The good agreement between experimental and numerical results verifies the effectiveness of the proposed BAAFM, demonstrating a stable and broadband acoustic focusing from 1500 to 4000 Hz. This study constructs a machine learning-assisted broadband achromatic optimization strategy, which paves the way for combining artificial intelligence with metastructure design and holds great promise for biomedical engineering and industrial manufacturing.