Learning the Basis: A Kolmogorov-Arnold Network Approach Embedding Green's Function Priors
Abstract
The Method of Moments (MoM) is constrained by the usage of static, geometry-defined basis functions, such as the Rao-Wilton-Glisson (RWG) basis. This letter reframes electromagnetic modeling around a learnable basis representation rather than solving for the coefficients over a fixed basis. We first show that the RWG basis is essentially a static and piecewise-linear realization of the Kolmogorov-Arnold representation theorem. Inspired by this insight, we propose PhyKAN, a physics-informed Kolmogorov-Arnold Network (KAN) that generalizes RWG into a learnable and adaptive basis family. Derived from the EFIE, PhyKAN integrates a local KAN branch with a global branch embedded with Green's function priors to preserve physical consistency. It is demonstrated that, across canonical geometries, PhyKAN achieves sub-0.01 reconstruction errors as well as accurate, unsupervised radar cross section predictions, offering an interpretable, physics-consistent bridge between classical solvers and modern neural network models for electromagnetic modeling.
Keywords
Cite
@article{arxiv.2511.08655,
title = {Learning the Basis: A Kolmogorov-Arnold Network Approach Embedding Green's Function Priors},
author = {Rui Zhu and Yuexing Peng and George C. Alexandropoulos and Wenbo Wang and Wei Xiang},
journal= {arXiv preprint arXiv:2511.08655},
year = {2026}
}
Comments
4 pages, 3 figures. Submitted to IEEE Antennas and Wireless Propagation Letters