Optimal design of topological waveguides by machine learning

Topological insulators supply robust edge states and can be used to compose novel waveguides to protect energy propagation against various defects. For practical applications, topological waveguides with a large working bandwidth and highly localized interface mode are desired. In the present work, mechanical valley Hall insulators are described by explicit geometry parameters using the moving morphable component method first. From the geometry parameters, artificial neural networks (ANN) are then well-trained to predict the topological property and the bounds of nontrivial bandgaps. Incorporating those ANN models, mathematical formulation for designing optimal mechanical topological waveguides can be solved efficiently, with an acceleration of more than 10,000 times than the traditional topology optimization approach.