Learning the Basis: A Kolmogorov-Arnold Network Approach Embedding Green's Function Priors
This work addresses the problem of inflexible basis functions in electromagnetic simulation for researchers and engineers, offering an incremental improvement by integrating neural networks with classical physics.
The paper tackles the limitation of static basis functions in electromagnetic modeling by introducing PhyKAN, a learnable basis approach that achieves sub-0.01 reconstruction errors and accurate radar cross section predictions on canonical geometries.
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.