Data-driven inverse design of a multiband second-order phononic topological insulator

Second-order phononic topological insulators (SPTIs) have sparked vast interest in manipulating elastic waves, owing to their unique topological corner states with robustness against geometric perturbations. However, it remains a challenge to develop multiband SPTIs that yield multi-frequency corner states using prevailing forward design approaches via trial and error, and most inverse design approaches substantially rely on time-consuming numerical solvers to evaluate band structures of phononic crystals (PnCs), showing low efficiency particularly when applied to different optimization tasks. In this study, we develop and validate a new inverse design framework, to enable the multiband SPTI by integrating data-driven machine learning (ML) with genetic algorithm (GA). The relationship between shapes of scatterers and frequency bounds of multi-order bandgaps of PnCs is mapped via developing artificial neural networks (ANNs), and a multiband SPTI with multi-frequency topological corner states is cost-effectively designed using the proposed inverse optimization framework. Our results indicate that the data-driven approach can provide a high-efficiency solution for on-demand inverse designs of multiband second-order topological mechanical devices, enabling diverse application prospects including multi-frequency robust amplification and confinement of elastic waves.