A Subdomain Physics-Informed Kolmogorov-Arnold Network with Chebyshev Representation for Inhomogeneous Superconducting Electromagnetic Analysis and Constitutive Identification

Accurate analysis of time-varying electromagnetic fields in superconductors under extreme operating conditions is crucial for the reliable design and operation of superconducting devices. A major challenge stems from the strong nonlinearity and field dependence of superconducting electromagnetic constitutive relations, particularly the critical current density, which are difficult to represent accurately using conventional analytical or numerical models. In this study, a subdomain Chebyshev-based physics-informed Kolmogorov-Arnold network (S-ChebPIKAN) is developed as an intelligent computational framework for solving time-varying electromagnetic problems in inhomogeneous superconducting systems and for identifying nonlinear electromagnetic constitutive relations. The computational domain is decomposed into superconducting and surrounding air subdomains, each modeled by an independent Kolmogorov-Arnold network and coupled through interface continuity constraints. Physics knowledge, including Maxwell’s equations, superconducting constitutive laws, magnetic boundary conditions, and interfacial constraints, is embedded into the learning process to ensure physical consistency and data efficiency. Numerical studies demonstrate that the proposed framework accurately predicts transient electromagnetic field distributions under applied magnetic-field and transport-current excitations, showing close agreement with finite element solutions and robust resolution of steep field gradients across material interfaces. Furthermore, under limited magnetic-field observations, the inverse modeling capability of S-ChebPIKAN enables reliable reconstruction of the magnetic-field-dependent critical current density, reproducing the decay behavior described by the Kim model. By treating the zero-field critical current density Jc0 and the power-law exponent n as trainable parameters, high-accuracy joint identification of key constitutive parameters is achieved. Overall, the proposed framework provides a data-efficient and physically informed intelligent solution for both forward electromagnetic analysis and constitutive parameter identification in inhomogeneous superconducting systems, offering a practical expert-system-oriented tool for superconducting material characterization and device modeling.