A physics-informed neural networks framework for electromagnetic field analysis in superconductors

Abstract

The accurate and efficient simulation of electromagnetic fields in superconductors is critical for the design and optimization of advanced applications such as high-field magnets and energy systems. Conventional numerical approaches primarily rely on the finite element method (FEM). In this work, a robust physics-informed neural networks (PINN) framework is developed to solve the coupled system of Maxwell’s equations and the nonlinear E–J power-law constitutive relation. A progressive validation strategy is adopted. Firstly, the magnetization of a superconducting bulk under an axial magnetic field is investigated to verify the capability of PINN in handling the strong nonlinearity electromagnetic behavior within a single domain. The PINN results show agreement with FEM. Secondly, the PINN framework is extended to multi-domain problems involving both superconducting and air regions under in-plane magnetic field and transport current. To address the severe resistivity discontinuity across the superconductor-air interface and improve training stability, a smooth transition function is introduced. The PINN solutions for these cases also achieve reasonable agreement against FEM. These results demonstrate that the proposed PINN framework serve as an effective, mesh-free collocation alternative for simulating nonlinear superconducting electromagnetics.