Small-Data Modeling of Electromagnetic Structures via Compressed Vector-Valued Kernel Ridge Regression

This paper presents a data-efficient surrogate modeling framework for electromagnetic structures and components based on a compressed formulation of vector-valued kernel ridge regression (VV-KRR). The method is intended for small-data regimes, where training samples generated through full-wave or circuit simulations are computationally expensive and therefore limited in number. By combining a compressed spectral formulation with a fully data-driven output-kernel construction, the proposed approach enables accurate multi-output modeling with reduced memory footprint, lower training cost, and improved computational scalability. The framework retains the ability of VV-KRR to capture cross-output correlations and to model high-dimensional responses, while featuring a simple training procedure and good numerical robustness. It is particularly attractive for simulation-driven design workflows in high-speed interconnect, RF, and microwave applications, where data generation is often the dominant computational cost. The method is validated on three representative electromagnetic modeling problems, demonstrating that accurate and robust surrogate models can be obtained even in data-constrained scenarios.