Deep learning-driven design of 1-D phononic crystals using surrogate and bandgap optimization models

Abstract

This study presents a method that combines two deep learning models—the surrogate model and the bandgap optimization model—to design 1-D Phononic Crystals. The surrogate model is trained to predict the bandgaps of Phononic Crystals, while the bandgap optimization model is used to determine their geometric parameters. The goal is to leverage deep learning’s ability to capture complex input-output relationships and exploit the inherent optimization capabilities of these models. To improve design accuracy and account for manufacturing constraints, a user-defined activation function is incorporated into the optimization model. Various loss functions are introduced to address different design objectives, such as maximizing the bandgap at a lower frequency or maximizing while aligning the center frequency of the bandgap with a specified value. The 1-D Phononic Crystal designed for bandgap maximization at lower frequencies using this method outperformed results predicted by a Genetic Algorithm. Unlike previous studies that often rely on deep learning only as a predictive tool or require external optimizers, our method uses a deep learning model directly as an optimization engine. The integration of customizable loss functions, user-defined physical constraints, and an unsupervised training approach enables versatile and efficient design without the need for labeled optimization datasets. The approach is readily extensible to 2-D and 3-D configurations, offering a versatile solution for advanced Phononic Crystal design.