Deep-learning-based framework for inverse design of a defective phononic crystal for narrowband filtering

Abstract

This paper proposes a deep-learning-based inverse design framework for a one-dimensional, defective phononic crystal (PnC) as a narrow bandpass filter under longitudinal elastic waves. The purpose of the design-optimization problem is to maximize the transmittance at the defect-band frequency, which is equal to the target frequency. The framework comprises three steps: (i) inverse design generation and filtering, (ii) forward analysis of frequencies and filtering, and (iii) forward analysis of transmittance and near-optimal design selection. Four deep-learning models are considered in the inverse model: a deep neural network, a tandem neural network, a conditional variation autoencoder, and a conditional generative adversarial network. The frameworks developed with each deep-learning model are evaluated using a test dataset and an arbitrarily defined defect-band frequency and phononic band-gap range. The results show that the frameworks proposed using the conditional variation autoencoder and the conditional generative adversarial network effectively present the best performance by solving the nonunique response-to-design mapping problem through probabilistic approaches. The deep-learning-based framework reduces the need for manual intervention and simplifies the inverse design process, making it a promising approach for finding the near-optimal design solution for the use of defective PnCs as narrow bandpass filters.