  The calculation of electromagnetic field distributions within structured
media is central to the optimization and validation of photonic devices. We
introduce WaveY-Net, a hybrid data- and physics-augmented convolutional neural
network that can predict electromagnetic field distributions with ultra fast
speeds and high accuracy for entire classes of dielectric photonic structures.
This accuracy is achieved by training the neural network to learn only the
magnetic near-field distributions of a system and to use a discrete formalism
of Maxwell's equations in two ways: as physical constraints in the loss
function and as a means to calculate the electric fields from the magnetic
fields. As a model system, we construct a surrogate simulator for periodic
silicon nanostructure arrays and show that the high speed simulator can be
directly and effectively used in the local and global freeform optimization of
metagratings. We anticipate that physics-augmented networks will serve as a
viable Maxwell simulator replacement for many classes of photonic systems,
transforming the way they are designed.
