A Neural Network-Based Model Order Reduction Methodology With Harmonic Forecasting for Parametric Nonlinear Magnetodynamic Simulations
Abstract
High-fidelity parametric simulations of nonlinear magnetodynamic systems are computationally demanding, making real-time and many-query applications impractical with conventional finite element methods (FEMs). While model order reduction (MOR) techniques address this challenge, extending them to nonlinear, time-dependent problems remains difficult, particularly when reduced-order differential equations must still be solved in the latent space. This article proposes a fully data-driven, nonintrusive MOR framework that combines a parametric autoencoder (AE) with a harmonic forecaster neural network, eliminating the need to solve any reduced-order dynamical equations. The AE compresses high-dimensional magnetodynamic field snapshots into a 4-D latent space, while the harmonic forecaster directly predicts the temporal evolution of latent trajectories by decomposing them into harmonic and learnable residual components. The framework is validated on a nonlinear inductor problem with three excitation waveforms, sinusoidal, triangular, and pulsewidth modulation (PWM), and assessed using a domain-anchored fivefold cross-validation strategy over a broad range of current amplitudes and frequencies. For sinusoidal and triangular excitations, the reduced-order model achieves mean field reconstruction errors of 0.68% and 0.80%, respectively, with mean flux linkage errors below 1%. For the significantly more challenging PWM case, mean field and flux linkage errors remain below 3.18%, demonstrating robustness under highly harmonic-rich excitations.