用可学习的基函数替代传统电磁建模中的固定基，提升精度与物理一致性。
Learning the Basis: A Kolmogorov-Arnold Network Approach Embedding Green's Function Priors
- 基于柯尔莫哥洛夫-阿诺德定理，设计可学习的物理感知基函数
- 在典型几何下重建误差低于0.01，无需标注即可准确预测雷达散射截面
- 适合需要物理可解释性的电磁仿真研究者，尤其关注传统与神经网络融合
矩量法（MoM）受限于静态、几何定义的基函数（如RWG基）。本文将电磁建模重构为可学习基表示，而非在固定基上求解系数。我们首先指出，RWG基本质上是柯尔莫哥洛夫-阿诺德表示定理的静态分段线性实现。受此启发，提出物理信息型柯尔莫哥洛夫-阿诺德网络（PhyKAN），将RWG推广为可学习、自适应的基函数族。该方法基于表面场积分方程（EFIE），融合局部KAN分支与嵌入格林函数先验的全局分支，确保物理一致性。在典型几何结构上，PhyKAN实现低于0.01的重建误差，并能无监督准确预测雷达散射截面（RCS），为经典求解器与现代神经网络模型之间提供可解释、物理一致的桥梁。
原文摘要 · Abstract (English)
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.
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