PINN-based resolution of inverse non-linear magnetostatic problems

Purpose This paper aims to propose a Physics Informed Neural Network (PINN) based method for the solution of inverse problems in magnetics, when the nonlinear characteristics of magnetic materials are included. Design/methodology/approach The proposed method is designed to estimate the current sources from a set of magnetic field measurement, in presence of nonlinear magnetic materials. The PINN constructed to solve this problem is based on the physics laws of magnetism that are used to solve the direct problem of calculating the field in a set of points given magnetization and currents. A loss function (backpropagating the error in the NN) evaluates the discrepancies between estimation and measurements and imposes the magnetic characteristics of the material. Findings The method has proven to be characterized by accuracy and low computational time if compared to more classical approaches which include regularization: in particular, the PINN that penalizes both measurement discrepancy and constitutive relation error can substantially improve source reconstruction in magnetostatics with magnetic materials. Originality/value To the best of the authors’ knowledge, the insertion of the constitutive error in the loss function proposed here is new and proves to be a step ahead in the utilization of PINN for the solution of nonlinear magnetic inverse problems. Furthermore, it paves the road for new applications in which inversion from data from complex systems can be a challenging task.