REAL-TIME DESIGN OF HIGHER-ORDER TOPOLOGICAL INSULATORS BY DIFFUSION MODEL

As a novel tool for wave manipulation, higher-order topological insulators can efficiently and robustly localize energy in low-dimensional space, exhibiting insensitivity to defects. Nevertheless, the fast design of higher-order topological insulators in photonic and phononic systems is still a challenge. In the present work, C_4v-symmetric continuum unit cells are explicitly described by the moving morphable voids method, and the concerned properties (topological properties and non-trivial bandgap width) are measured by the band theory and symmetry indicators. Based upon these, a dataset of higher-order topological insulators is constructed, incorporating geometric parameters, normalized bandgap width, and topological property indicators. A real-time design paradigm is proposed utilizing a denoising diffusion probabilistic model (DDPM). Compared to design paradigms using other generative models, DDPM effectively avoids issues such as training instability and low fidelity in generation. This paradigm enables accurately and fast inverse design of mechanical higher-order topological insulators based on target requirements or maximizing the non-trivial bandgap width. Applying this developed inverse design paradigm, the average relative error for generating the desired designs on a desktop computer is within 3.5%, with an average generation time of only 0.01 seconds, which significantly improves the design efficiency by 6 to 7 orders of magnitude compared with the traditional inverse design methods. By using the Wasserstein distance to measure the diversity of inverse design results, this paradigm exhibits higher diversity compared to the optimization design results obtained by deep learning based surrogate model. In addition, the generated designs have explicitly described geometric information, so they can be directly integrated with CAD/CAE software, avoiding the post-processing step required in implicit description methods. This real-time design paradigm based on DDPM can be easily extended to inverse design of multi-physical topological materials and other types of metamaterials, laying the foundation for constructing databases for photonic and phononic topological materials.