Convolutional neural network driven design optimization of acoustic metamaterial microstructures

Abstract

The design of broadband mechanical metamaterials in the context of acoustics can be driven by the invariance of the wave equation under a set of special coordinate transformations called transformation acoustics. A program of homogenization to design the metamaterial structure can be derived from these transformation functions subject to geometric constraints from the metamaterial’s intended application. The limits of homogenization in a nonperiodic, nonlinear environment however must be accounted for and corrected. This can be done by means of nonlinear manifold interpolation methods, the feedback into which is driven by the scattered wave field in the ambient medium. The feedback is minimized using statistical and machine learning techniques, dictating the final metamaterial structure. The performance of this algorithmic method is compared against a “brute force” optimization approach driven by a convolutional neural network with no transformation of the underlying wave equation.