Learning the Physics of All-Dielectric Metamaterials with Deep Lorentz Neural Networks

Deep neural networks (DNNs) have shown marked achievements across numerous research and commercial settings. Part of their success is due to their ability to “learn” internal representations of the input (x) that are ideal to attain an accurate approximation ((Formula presented.)) of some unknown function (f) that is, y = f(x). Despite their universal approximation capability, a drawback of DNNs is that they are black boxes, and it is unknown how or why they work. Thus, the physics discovered by the DNN remains hidden. Here, the condition of causality is enforced through a Lorentz layer incorporated within a deep neural network. This Lorentz NN (LNN) takes in the geometry of an all-dielectric metasurface, and outputs the causal frequency-dependent permittivity (Formula presented.) and permeability (Formula presented.). Additionally, this LNN gives the spatial dispersion (k) inherent in the effective material parameters, as well as the Lorentz terms, which constitute both (Formula presented.) and (Formula presented.). The ability of the LNN to learn metasurface physics is demonstrated through several examples, and the results are compared to theory and simulations.