Higher-order topological insulators by ML-enhanced topology optimization

Abstract

Energy in lower dimensions, such as edges or corners, can be robustly confined by the higher-order topological insulators (HOTIs) against defects. Being promising for wave manipulation, the unique property of HOTIs is protected by the associated topological invariant and bulk band. Nevertheless, it is still challenging to fast design topologically nontrivial continuum unit cells with highly localized edge/corner modes in photonic and phononic systems. In the present work, with the help of a multitask learning model simultaneously predicting the discrete-valued topological invariant and continuum-valued bandgap range, a fast design framework is developed using an explicit topology optimization method for mechanical HOTIs. In the solution process, the machine learning model and backpropagation algorithm are integrated into a MultiStart solver to accelerate the design efficiency by 3–4 orders than the traditional topology optimization method. Furthermore, a novel programmable mechanical imaging device illustrates the applications of the optimized HOTI with highly localized corner states. This AI-enhanced design paradigm can be easily extended for the fast design of optimized topological materials among various physical systems.