A three-stage multi-fidelity physics-informed neural network for control-oriented electromagnetic force surrogate modeling in PM-EDW systems

Control-oriented electromagnetic-force surrogates must be fast enough for repeated in-loop evaluation while preserving their encoded physical constraints beyond the conditions used for calibration. We develop a three-stage multi-fidelity physics-informed neural network (PINN) for permanent-magnet electrodynamic suspension (PM-EDS). Analytical field relations first define the relevant force constraints; a field-informed module then identifies interpretable constraint parameters; finally, a force-level surrogate embeds gap decay, lift boundedness, and lift–drag coupling in its output structure. The model is evaluated against analytical, finite-element, and calibration-unseen static experiments at three air gaps. It does not uniformly outperform an unconstrained multilayer perceptron (MLP) in average error, but it enforces its calibrated C2 lift envelope by construction and remains competitive across the evaluated force domains. In a FEM-dominant near-saturation control simulation, the PINN maintains zero exceedances of a common calibrated C2 model-reference envelope over all tested stress levels, whereas the MLP and analytical lookup exceed that reference. These results identify the contribution as an accuracy–feasibility trade-off under the tested near-boundary conditions, not as a guarantee of universally lower prediction or tracking error. The evidence supports multi-gap static prediction and simulation-level constraint-consistency assessment; hardware closed-loop readiness remains to be established.