Solving Numerical Green’s Function of 3-D Randomly Distributed Dielectric Targets Using Kolmogorov-Arnold Networks

Numerical Green’s functions (NGF) encapsulate the effects of complex media as pre-calculated functions, significantly reducing the number of unknowns in electromagnetic scattering problems. However, recalculations are often required when scatterers’ positions change. In this article, a neural network-accelerated NGF method is proposed for three-dimensional (3-D) randomly distributed dielectric targets. This method enables real-time NGF output of targets at arbitrary positions within the domain. By analyzing three cases—a single dielectric target, a group with identical targets, and a group with different targets—the field and source, along with the spatial distribution and properties of scatterers, are preprocessed as input of the Kolmogorov-Arnold Network (KAN). The incorporation of physical information allows the network to effectively capture the impact of scatterers’ position variations on the NGF. Additionally, feature extraction is employed to enhance the efficiency and reduce the mean squared error (MSE) of KAN by extracting the unknown NGF secondary term as the acceleration part. The proposed neural network-accelerated NGF method is applied to the analysis of 3-D metamaterial scattering and the approximate modeling of indoor wireless channels. Numerical results demonstrate that the trained network model can output the NGF for arbitrarily distributed targets, significantly reducing the computational cost of scattered field calculations while maintaining low numerical errors.