Deep learning for Dirac dispersion engineering in sonic crystals

Band structure and Dirac degeneracy are essential features of sonic crystals/acoustic metamaterials to achieve advanced control of exciting wave effects. In this work, we explore a deep learning approach for the design of phononic crystals with desired dispersion. A plane wave expansion method is utilized to establish the dataset relation between the structural parameters and the energy band features. Subsequently, a multilayer perceptron model trained using the dataset can yield accurate predictions of wave behavior. Based on the trained model, we further impose a re-learning process around a targeted frequency, by which Dirac degeneracy and double Dirac degeneracy can be embedded into the band structures. Our study enables the deep learning approach as a reliable design strategy for Dirac structures/metamaterials, opening up the possibilities for intriguing wave physics associated with Dirac cone.