Modular Meshless Electromagnetic Simulation Using KAN-Based Physics-Informed Neural Networks

A novel meshless electromagnetic (EM) simulation framework based on Physics-Informed Neural Networks (PINNs), enhanced by the integration of Kolmogorov–Arnold Networks (KANs) is presented. The proposed method addresses both electrostatic and electrodynamic problems governed by Laplace and Helmholtz equations, respectively. A modular and interpretable simulation architecture is developed using KAN-PINNs which enables accurate field learning in multilayered printed circuit boards (PCBs) with spatially varying permittivity. Three canonical structures: an electrostatic box, a parallel-plate transmission line (TL) and a stripline TL are modeled to demonstrate the validity of the method. The results are validated against commercial full-wave solvers showing excellent agreement with normalized root-mean-square errors (RMSE) below 0.1. Moreover, a 4-layer PCB structure is simulated at 100 MHz to demonstrate the method's capability at higher frequencies. For this case, the model achieves a normalized RMSE of 0.153 while reducing simulation time by a factor of three compared to numerical solvers. The proposed framework provides a scalable and fully mesh-free alternative to traditional electromagnetic solvers. This introduces new potential for efficiently simulating complex PCB structures in EMI applications.