Abstract
AbstractThe prediction and design of photonic features have traditionally been guided by theory-driven computational methods, spanning a wide range of direct solvers and optimization techniques. Motivated by enormous advances in the field of machine learning, there has recently been a growing interest in developing complementary data-driven methods for photonics. Here, we demonstrate several predictive and generative data-driven approaches for the characterization and inverse design of photonic crystals. Concretely, we built a data set of 20,000 two-dimensional photonic crystal unit cells and their associated band structures, enabling the training of supervised learning models. Using these data set, we demonstrate a high-accuracy convolutional neural network for band structure prediction, with orders-of-magnitude speedup compared to conventional theory-driven solvers. Separately, we demonstrate an approach to high-throughput inverse design of photonic crystals via generative adversarial networks, with the design goal of substantial transverse-magnetic band gaps. Our work highlights photonic crystals as a natural application domain and test bed for the development of data-driven tools in photonics and the natural sciences.
Highlights
The confluence of an exceptional abundance of data and computational resources has enabled techniques of machine learning (ML), especially deep neural networks [1, 2], to revolutionize fields across computer science, ranging from image analysis [3,4,5,6] and natural language processing [7,8,9,10] to decision making [11, 12]
We built a data set of 20,000 twodimensional photonic crystal unit cells and their associated band structures, enabling the training of supervised learning models
We demonstrate a high-accuracy convolutional neural network for band structure prediction, with orders-of-magnitude speedup compared to conventional theory-driven solvers
Summary
The confluence of an exceptional abundance of data and computational resources has enabled techniques of machine learning (ML), especially deep neural networks [1, 2], to revolutionize fields across computer science, ranging from image analysis [3,4,5,6] and natural language processing [7,8,9,10] to decision making [11, 12]. Provided the assumed material response and geometric features of the underlying structures are accurate, such calculations generally agree extremely well with optical measurements, resembling, effectively, “numerical experiments” (in contrast to e.g. electronic structure calculations that typically exploit physical approximations, i.e. not merely a truncated basis, to overcome the computational challenges posed by manybody electron–electron interactions) This makes photonic systems ideal test beds for exploring the applications of data-driven techniques in realistic physical systems; and for developing new ML techniques for the natural sciences in general. Our results establish PhCs as a natural test bed for ML techniques applied to scientific problems and demonstrate that both forward and inverse problems in PhC-design are amenable to datadriven approaches
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