G-PIFNN: A Generalizable Physics-informed Fourier Neural Network Framework for Electrical Circuits

Abstract: Physics-Informed Neural Networks (PINNs) have advanced the data-driven solution of differential equations (DEs) in dynamic physical systems, yet challenges remain in explainability, scalability, and architectural complexity. This paper presents a Generalizable Physics-Informed Fourier Neural Network (G-PIFNN) framework that enhances PINN architectures for efficient and interpretable electrical circuit analysis. The proposed G-PIFNN introduces three key advancements: (1) improved performance and interpretability via a physics activation function (PAF) and a lightweight Physics-Informed Fourier Neural Network (PIFNN) architecture; (2) automated, bond graph (BG) based formulation of physics-informed loss functions for systematic differential equation generation; and (3) integration of intra-circuit and cross-circuit class transfer learning (TL) strategies, enabling unsupervised fine-tuning for rapid adaptation to varying circuit topologies. Numerical simulations demonstrate that G-PIFNN achieves significantly better predictive performance and generalization across diverse circuit classes, while significantly reducing the number of trainable parameters compared to standard PINNs.