Surrogate modeling of inductance in axial active magnetic bearings using data-driven and physics-informed neural networks

In active magnetic bearing (AMB) systems, accurate modeling of nonlinear electromagnetic effects is essential for high-fidelity simulation and control design. Conventional approaches rely on either analytical approximations, which are often too simplified to capture the full nonlinear behavior, or on finite element method (FEM)-based lookup tables, which require computationally expensive interpolation and exhibit poor generalization in sparsely sampled regions. This motivates efficient surrogate modeling approaches that preserve FEM-level accuracy while enabling scalable, continuous evaluation. This paper proposes a physics-informed neural network (PINN) approach for inductance modeling in axial AMBs, combining data-driven learning with electromagnetic circuit physics. Two architectures are developed for comparison: a purely data-driven NN and a PINN. The main novelty of this work is a physics-informed learning formulation in which the actuator voltage equation as an ordinary differential equation (ODE) constraint, is embedded into the PINN loss function, enabling consistent enforcement of the nonlinear electrical dynamics and the coupled dependence of inductance on airgap position and coil current. The trained models are validated under open- and closed-loop conditions with position and inner current control, followed by offline experimental verification using data collected from a real AMB setup. Comparative analysis with a data-driven NN, Polynomial Regression, and Gaussian Process Regression surrogate models demonstrates that incorporating physics-based constraints into the loss function improves model accuracy and consistency, particularly in sparsely sampled regions. The proposed PINN thus provides a physics-consistent and computationally efficient surrogate model for axial AMB systems, replacing conventional FEM-based lookup tables.