Prediction multimodal optical responses for ultrafast plasmonic based functional universal approximation theorem with exponential data efficiency
Yulu Qin, Haoyang Cheng, Haixia Zheng, Hanmin Hu, Xiaolong Zhou · Optics Express · 2025
Machine learning offers efficient alternatives to traditional solvers for modeling nonlinear relationships between nanophotonic structures and their optical responses. However, neural network (NN)-based methods typically represent functional data as high-dimensional pointwise vectors without incorporating structural priorities, which limits their ability to capture the smoothness and continuity of such data and results in a strong dependence on large training datasets. To address this challenge, we propose a modeling framework based on the functional universal approximation (FUA) theorem, which leverages functional data analysis (FDA) to efficiently learn nonlinear function-on-scalar mappings by explicitly modeling functional structure. We validate the method on an aluminum nano ring-disk dimer, accurately predicting absorption, scattering, near-field spectra, and time-resolved electric fields using only 300 training samples, achieving R 2 values of 0.86, 0.84, 0.96, and 0.98, respectively. Compared to NN models, FUA shows superior data efficiency, robustness, and generalization, offering a promising approach for small-sample inverse design in nanophotonics.