Machine Prediction of Topological Transitions in Photonic Crystals
Bei Wu, Kun Ding, C.T. Chan, Yuntian Chen
Abstract
Neural networks based on machine learning can interpolate well within the training dataset, but their ability to extrapolate is severely limited by fundamental issues such as the bias-variance trade-off. Here we introduce the concept of an operator parameter space consisting of physical entities encoded with Maxwell's equations to improve the networks' capability to generalize beyond their training set. We illustrate the idea with photonic crystals, and show that the network trained with operator parameters yields remarkably accurate predictions of the topological transitions both within and beyond the training physical space. Such concepts can be generalized to higher-dimensional wave structures by choosing the appropriate operator parameters.