  The data sciences revolution is poised to transform the way photonic systems
are simulated and designed. Photonics are in many ways an ideal substrate for
machine learning: the objective of much of computational electromagnetics is
the capture of non-linear relationships in high dimensional spaces, which is
the core strength of neural networks. Additionally, the mainstream availability
of Maxwell solvers makes the training and evaluation of neural networks broadly
accessible and tailorable to specific problems. In this Review, we will show
how deep neural networks, configured as discriminative networks, can learn from
training sets and operate as high-speed surrogate electromagnetic solvers. We
will also examine how deep generative networks can learn geometric features in
device distributions and even be configured to serve as robust global
optimizers. Fundamental data sciences concepts framed within the context of
photonics will also be discussed, including the network training process,
delineation of different network classes and architectures, and dimensionality
reduction.
