Deep Learning Enables Accurate Sound Redistribution via Nonlocal Metasurfaces

Conventional acoustic metasurfaces are constructed with ``locally'' gradient phase-shift profiles provided by subunits. The local strategy implies the ignorance of the mutual coupling between subunits, which limits the efficiency of targeted sound manipulation, especially in complex environments. By taking into account the ``nonlocal'' interaction among subunits, nonlocal metasurface offers an opportunity for accurate control of sound propagation, but the requirement of the consideration of gathering coupling among all subunits, not just the nearest-neighbor coupling, greatly increases the complexity of the system and therefore hinders the explorations of functionalities of nonlocal metasurfaces. In this work, empowered by deep-learning algorithms, the complex inverse gathering coupling can be learned efficiently from the preset dataset so that the inverse mechanism of nonlocal metasurfaces can be described effectively. As an example, we demonstrate that nonlocal metasurfaces, which can redirect an incident wave into multichannel reflections with arbitrary energy ratios, can be accurately predicted by deep-learning algorithms. Compared to the theory, the relative error of the energy ratios is less than 1%. Furthermore, experiments witness three-channel reflection with three types of energy ratios of (1, 0, 0), (1/2, 0, 1/2), and (1/3, 1/3, 1/3), proving the validity of the deep-learning-enabled nonlocal metasurfaces. Our work might blaze an alternative trail in the design of acoustic functional devices, especially for the cases containing complex wave-matter interactions.