Inverse Design of Customized Dispersion Curves in Phononic Crystals by Physics-Informed Neural Networks With Elastic Wave Field Embedding

Leveraging the ability to customize dispersion characteristics in phononic crystals (PnCs) enables the arbitrary control of elastic or acoustic wave propagation. However, the whole dispersion involves complex profuseness eigenstates from low frequencies to high ones, while the wave vectors should cover the small wave vectors to the large ones. Here, a physics-informed framework is introduced for forward prediction and inverse design of PnCs with customized dispersion relations. By integrating the elastic wave equation and elastic wave field information into the learning process, the proposed approach ensures both high computational efficiency and enhanced interpretability, enabling customized dispersion engineering of PnCs and thereby achieving arbitrary required whole dispersion relations covering the total frequency range and wave vectors. Furthermore, the method effectively handles diverse kinds of dispersion curves in PnCs, including the dispersion curves with Bragg scattering, local resonance, prescribed group velocities, and modal degeneracy. Numerical results show that the present physics-informed design methodology has an obvious advantage of purely data-driven approach in the aspect of design accuracy and data efficiency, constructing the meticulous elastic/acoustic wave propagation in PnCs or periodic structures.