Physics-Guided Hierarchical Neural Networks for Maxwell's Equations in Plasmonic Metamaterials.

While machine learning (ML) has found multiple applications in photonics, traditional "black box" ML models typically require prohibitively large training data sets. Generation of such data, as well as the training processes themselves, consume significant resources, often limiting practical applications of ML. Here, we demonstrate that embedding Maxwell's equations into ML design and training significantly reduces the required amount of data and improves the physics-consistency and generalizability of ML models, opening the road to practical ML tools that do not need extremely large training sets. The proposed physics-guided machine learning (PGML) approach is illustrated on the example of predicting complex field distributions within hyperbolic meta-material photonic funnels, based on multilayered plasmonic-dielectric composites. The hierarchical network design used in this study enables knowledge transfer and points to the emergence of effective medium theories within neural networks.