Simplifying nano-photonic structure inverse design with neural networks: a study of statistical and computational complexity

This work presents a comprehensive investigation aimed at identifying the most streamlined neural network architecture for the inverse design of nanophotonic structures. In pursuit of this objective, we delve into the statistical and computational complexities inherent in neural network design, contextualized within the realm of nanophotonic structures, as defined by their design complexity, e.g., the number of constituent parameters. The study encompasses two critical dimensions: statistical complexity, where we explore the optimal quantity of training data, and computational complexity, where our aim is the study of the required computation and model complexity for accurately modeling the input-output relation in a class of nanophotonic structures. Through the integration of these two facets, we will determine the simplest neural network configuration for the given class of nanophotonic structures, facilitating efficient and accurate inverse design, and understanding the effect of design parameters on the output response complexity. In addition to reporting the details of this novel technique, we will show its implementation for two important classes of nanophotonic devices.