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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 network 

We develop a hierarchical approach to building a Physics-guided neural network (PGNN) for scalable solutions of Maxwell equations with high spatial resolution and illustrate the developed formalism on a metamaterial photonic funnel example. 

Four different biorenewable methacrylated/acrylated monomers, namely, methacrylated fatty acid (MFA), methacrylated eugenol (ME), isobornyl methacrylate (IM), and isobornyl acrylate (IA) were employed as reactive diluents (RDs) to replace styrene (St) in a maleinated acrylated epoxidized soybean oil (MAESO) resin to produce bio-based thermosetting resins using free radical polymerization. The curing kinetics, gelation times, double bond conversions, thermal–mechanical properties, and thermal stabilities of MAESO-RD resin systems were characterized using DSC, rheometer, FT-IR, DMA, and TGA. The results indicate that all four RD monomers possess high bio-based carbon content (BBC) ranging from 63.2 to 76.9% and low volatilities (less than 7 wt% loss after being held isothermally at 30 °C for 5 h). Moreover, the viscosity of the MAESO-RD systems can be tailored to acceptable levels to fit the requirements for liquid molding techniques. Because of the introduction of RDs to the MAESO resin, the reaction mixtures showed an improved reactivity and an accelerated reaction rate. FT-IR results showed that almost all the CC double bonds within MAESO-RD systems were converted. The glass transition temperatures ( T g ) of the MAESO-RDs ranged from 44.8 to 100.8 °C, thus extending the range of application. More importantly, the T g of MAESO-ME resin (98.1 °C) was comparable to that of MAESO-St resin (100.8 °C). Overall, this work provided four potential RDs candidates to completely replace styrene in the MAESO resin, with the ME monomer being the most promising one.