Physics-Constrained Neural Network for Metasurface Optical Response Prediction

Abstract

A physics-constrained neural network is presented for predicting the optical response of metasurfaces. Our approach incorporates physical laws directly into the neural network architecture and loss function, addressing critical challenges in the modeling of metasurfaces. Unlike methods that require specialized weighting strategies or separate architectural branches to handle different data regimes and phase wrapping discontinuities, this unified approach effectively addresses phase discontinuities, energy conservation constraints, and complex gap-dependent behavior. We implement sine-cosine phase representation with Euclidean normalization as a non-trainable layer within the network, enabling the model to account for the periodic nature of phase while enforcing the mathematical constraint $\sin^2 ϕ+ \cos^2 ϕ= 1$. A Euclidean distance-based loss function in the sine-cosine space ensures a physically meaningful error metric while preventing discontinuity issues. The model achieves good, consistent performance (e.g., coefficient of determinations above 0.9) with small, imbalanced datasets of 580 and 1075 data points, compared to several thousand typically required by alternative approaches. This physics-informed approach preserves physical interpretability while reducing reliance on large datasets and could be extended to systems involving periodic or wrapped quantities.