Physics-guided hierarchical neural networks for Maxwell's equations in plasmonic metamaterials

TL;DR

This paper introduces a physics-guided machine learning approach that embeds Maxwell's equations into neural networks, reducing data needs and enhancing model accuracy for plasmonic metamaterials.

Contribution

The study presents a novel hierarchical neural network architecture that incorporates Maxwell's equations, improving data efficiency and physics consistency in modeling complex photonic structures.

Findings

Reduces training data requirements significantly

Improves physics consistency and generalizability of ML models

Demonstrates effectiveness on hyperbolic metamaterial photonic funnels

Abstract

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 metamaterial 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.