Design of aluminum plate phononic crystals with wide bandgaps via free-form shape optimization using deep neural networks

Phononic crystals (PnCs) with a broad bandgap have been the subject of extensive research, particularly for their capacity to manipulate elastic waves efficiently. However, the explored design space remains relatively limited, and the shapes under consideration are often relatively simple. This study optimizes a free-form hole shape for square and hexagonal lattice aluminum plate PnCs with high relative bandgaps (i.e., ratio of bandgap to its center frequency). Optimization is implemented by leveraging the predictive capabilities of deep neural networks (DNNs). For both types of lattices, an initial training dataset is made up of 20,000 randomly generated PnCs unit cells, each containing a symmetric smooth hole. The relative bandgap is subsequently evaluated using the Finite Element Method (FEM). For each lattice, one Deep Neural Network (DNN) is trained to predict the relative bandgap, while another DNN is used to classify whether the bandgap exists. The predictive power of DNNs is exploited to search for design candidates with high relative bandgaps using the genetic optimization algorithm (GOA). The relative bandgaps of new candidates are determined and validated using FEM. The results of these analyses are then utilized to update the DNNs through active learning (AL) techniques. As a result, the relative bandgaps of the progressively refined hole shapes for square and hexagonal lattices are 2.382 and 10.383 times larger, respectively, than those of circular holes.