Machine Learning in Interpolation and Extrapolation for Nanophotonic Inverse Design

The algorithmic design of nanophotonic structures promises to significantly improve the efficiency of nanophotonic components due to the strong dependence of electromagnetic function on geometry and the unintuitive connection between structure and response. Such approaches, however, can be highly computationally intensive and do not ensure a globally optimal solution. Recent theoretical results suggest that machine learning techniques could address these issues as they are capable of modeling the response of nanophotonic structures at orders of magnitude lower time per result. In this work, we explore the utilization of artificial neural network (ANN) techniques to improve the algorithmic design of simple absorbing nanophotonic structures. We show that different approaches show various aptitudes in interpolation versus extrapolation, as well as peak performances versus consistency. Combining ANNs with classical machine learning techniques can outperform some standard ANN techniques for forward design, both in terms of training speed and accuracy in interpolation, but extrapolative performance can suffer. Networks pretrained on general image classification perform well in predicting optical responses of both interpolative and extrapolative structures, with very little additional training time required. Furthermore, we show that traditional deep neural networks are able to perform significantly better in extrapolation than more complicated architectures using convolutional or autoencoder layers. Finally, we show that such networks are able to perform extrapolation tasks in structure generation to produce structures with spectral responses significantly outside those of the structures on which they are trained.