Inverse design of multiband higher-order elastic topological insulators via generative deep learning

Higher-order elastic topological insulators with corner states exhibit significant potential for robust elastic wave localization. Nevertheless, it is quite challenging to design multiband topological structures on demand via traditional empirical methods that rely on trial and error. Here, we present a novel inverse design paradigm for multiband higher-order elastic topological insulators based on deep learning techniques. A generative model that enables a vast design space is first developed, incorporating a rich series of unit cell patterns with the desired crystalline symmetry and fabrication feasibility. Thereafter, a predictive model is constructed to efficiently forecast the dispersion characteristics of any given unit cell, thereby accelerating the discovery of potential multiband topological structures. We demonstrate the effectiveness and reusability of the proposed design framework through diverse examples of multiband higher-order elastic topological insulators with multi-frequency corner states. This deep learning-driven approach addresses the limitations of conventional inverse design methods, which often require computationally expensive simulations and lack flexibility to variable design tasks. Our work underscores great potential of deep learning techniques for the inverse design of high-performance topological metamaterials.