Frequency-Domain Physics-Informed Neural Networks for Parameter Estimation

While physics-informed neural networks (PINNs) are commonly employed for time-domain problems, this work extends their application to the frequency domain for parameter estimation. The framework integrates the governing equation into the neural network (NN) training loss function by using a composite complex domain formulation to enforce data consistency, minimize physics residuals, and respect parameter bounds. The methodology is presented as a transfer function-based formulation, whose parameters can be estimated from available data. The effectiveness of the methodology is validated through both simulation and experimental datasets on axial active magnetic bearing (AMB) systems, which are open-loop unstable and thus make frequency-domain parameter estimation particularly relevant. The results show excellent agreement between measured and predicted responses. Furthermore, the proposed approach is compared with an existing frequency-domain identification approach. PINN-based estimation of physical parameters is closer to reference values due to physics residual and parameter bounds. The findings validate the proposed methodology, which indicates that the PINN-based frequency-domain framework can accurately estimate system parameters, demonstrating its accuracy and robustness for physics-constrained learning in the frequency domain.