Abstract

Deep-learning-based surrogate models have emerged as an efficient alternative to traditional numerical methods, significantly reducing the computational overhead in band-structure analysis and inverse design of phononic crystals (PnCs). While many studies have successfully employed these models to both one-dimensional (1D) and two-dimensional (2D) PnCs, they have primarily been confined to unit-cell level analysis using deep Neural Networks (DNNs) or Convolutional Neural Networks (CNNs). In contrast, evaluating defective PnCs, which involve structural irregularities within a supercell, requires the ability to accommodate different numbers of unit cells. Conventional DNN and CNN models encounter fundamental limitations in this context due to their fixed-scale input dimensions. Although recent work has introduced Transformer-based architectures to mitigate these challenges in 1D PnCs, such an approach has not yet been investigated for 2D PnC systems.

In this study, a comparative evaluation of surrogate modeling approaches is conducted for 2D PnC systems encompassing a range of unit cell counts and defect configurations. To address varying input scales, the focus lies on architectures with inherent scalability, specifically utilizing Transformer-based or graph-based structures that can process flexible lengths and topological connections. Within these models, structural features are first compressed at the unit-cell level through CNN or Variational Autoencoder (VAE) layers, encoding high-dimensional geometric data into essential latent representations. The resulting latent features are then integrated by the scalable backbone to capture unit-cell interactions and dispersion characteristics from the localized point defects. Such formulation enables the model to effectively map how specific defect configurations alter the overall dispersion behavior of the system.

For training surrogate models, each 2D PnC structure is generated as grid-based image data to ensure high-fidelity mapping of complex material distributions. To facilitate a robust analysis, a wide variety of geometries are produced by mapping randomized control points using polar and step functions into a symmetric unit cell, resulting in an extensive dataset that encompasses various structural irregularities. The diverse collection of configurations serves as the foundation for a rigorous validation of each model's evaluated accuracy and response: accuracy in predicting complex band structures, computational efficiency during and inference, and explainability regarding how the models perceive structural perturbations. By examining how different surrogate models process these discretized geometries, either as sequences of compressed patches or as interaction nodes, this research aims to provide practical guidance for selecting and designing robust architectures for reliable dispersion-relation prediction in defective 2D PnCs.