Transformer-based prediction of dispersion relation and transmittance in phononic crystals

Abstract

This study presents PnCFormer, a transformer-based surrogate model tailored for one-dimensional phononic crystals (1D PnCs) with structural variability. The model is designed to accommodate variations in material properties, geometric dimensions, and the number and arrangement of unit cells, including defects. To address the challenge of variable-length inputs (a total number of unit cells), the system employs a padding and masking strategy, complemented by an enhanced feature embedding (EFE) that incorporates both basic given and wave-relevant engineered features. A frequency-aware decoder that utilizes frequency-domain queries (FDQ) facilitates precise prediction of both dispersion relations and transmittance frequency response functions (FRFs). PnCFormer is trained on a substantial analytically generated dataset encompassing 168 PnC configurations. The model demonstrates excellent agreement with ground-truth results, accurately capturing band gaps and defect bands in dispersion relations, and nearly zero and peak values in transmittance FRFs. The framework’s primary contributions are threefold: first, the integration of EFE for physically informed embedding, second, the implementation of FDQ for spectral prediction in parallel, and third, generalizable architecture that is adept at managing various structural arrangements. These innovations enable PnCFormer to perform rapid, high-fidelity spectral analysis across diverse 1D PnC designs. The model’s flexibility and accuracy suggest significant potential for applications in enhanced ultrasonic sensors and actuators for nondestructive evaluation, medical imaging, and prognostics and health management.