Deep learning of plausible bandgaps in dispersion curves of phononic crystals

Phononic crystals represent an interesting class of metamaterials that can be utilized to regulate or manipulate vibration, sound propagation, and thermal transport. Their useful features mainly arise from the bandgaps in their dispersion curves, preventing the passage of waves within specific frequency ranges. However, it is often costly and time-consuming to obtain the dispersion curves, and the reverse engineering of phononic crystals to have pre-defined bandgaps possesses even greater challenges. In this research, we address this issue by employing a deep artificial neural network to predict the bandgap ratio and the characteristics of plausible bandgaps, focusing on the localized resonance in columnar phononic crystals. We utilized two geometric parameters, i. e. the ratio of diameter and height of the cylindrical resonators relative to the lattice constant, achieving a determination coefficient of 0.9993 for predicting the characteristics of the bandgaps and 0.9827 for predicting the bandgap ratio. To verify the model and better understand its behavior, we introduce Shapley values. These values provide a comprehensive insight into how each geometric parameter influences the predicted bandgap ratios.