Gradient Networks for Universal Magnetic Modeling of Synchronous Machines

Incorporating hysteresis and eddy currents into finite element simulations of laminated-core electrical machines is computationally challenging. Resolving the fields inside the laminations at each integration point and at every nonlinear iteration leads to computational costs several orders of magnitude higher than anhysteretic simulations, making such approaches impractical for design applications. Conversely, simplified models accounting only for magnetic saturation are becoming increasingly inadequate as electrical machine topologies and operating conditions grow in complexity. In this context, machine learning surrogate modeling has emerged as a promising alternative, offering efficient and accurate approximations of complex electromagnetic behaviors. In this paper, a recurrent neural network is trained as a surrogate of a laminated-core material model for an isotropic laminated core, and is integrated into realistic two-dimensional magnetodynamic finite element simulations based on a magnetic vector potential formulation. The proposed approach achieves excellent agreement with the reference laminated-core model while limiting the computational cost to about twice that of an anhysteretic simulation. By training the recurrent neural network on a sufficiently diverse set of artificially generated magnetic field sequences designed to mimic those encountered in electrical machine simulations, the proposed approach can be readily applied across a wide range of finite element simulations. Furthermore, the trained surrogate model is provided as a standalone component that can be easily incorporated into existing computational frameworks. It is publicly available at https://gitlab.onelab.info/getdp/lamnet.

Wound rotor synchronous motors have emerged as a strong alternative that eliminates dependence on REEs. However, WRSM design requires the simultaneous optimization of numerous geometric and electromagnetic parameters, and the high computational cost of conventional finite element analysis severely limits the rapid exploration of the large parameter space. Although there are machine-learning-based surrogate modeling studies in the literature, they generally compare only a limited number of models, exclude deep learning architectures, and do not provide a comprehensive benchmark specific to WRSM. In this study, the performance of a total of eight machine learning and deep learning models from four different algorithmic families was systematically compared for the prediction of WRSM torque and motor efficiency. On a dataset of 3351 samples generated using Latin Hypercube Sampling in the Motor-CAD simulation environment, each model was trained with 10 different random seed values and tuned via Optuna hyperparameter optimization. Different from the existing literature, this study jointly offers a broad model spectrum including recent deep learning architectures such as FT Transformer, a multi-seed reproducibility protocol, and a Pareto analysis of the computational cost-accuracy trade-off. The results revealed that neural-network-based models systematically outperform tree-based models. The FT-Transformer model achieved the highest single-model accuracy with R^2 = 0.9928, producing predictions in 0.33 milliseconds and thus obtaining several orders of magnitude speedup compared to FEA. Model performances were evaluated in a multidimensional manner using R^2, MAE, RMSE, and MAPE metrics.

Magnetic components in high-frequency, high-power-density converters are increasingly driven by non-sinusoidal flux-density waveforms with fast transitions, minor-loop operation, dc bias, and temperature variation. Under these conditions, steady-state core-loss formulas and single-valued material curves cannot fully capture transient magnetization responses. This work proposes the Physics-Informed Hybrid Neural Operator (PI-HNO), a compact material-specific neural model with B-H energy-consistency regularization for core-loss-oriented transient magnetization prediction. Given the measured B(t)-H(t) history, the input B(t) series over the prediction interval and operating-condition information, PI-HNO predicts the H(t) series and the corresponding reconstructed B-H trajectory. The model integrates a local recurrent branch for boundary-state representation and rate-dependent response evolution with a Preisach-inspired global branch that extracts waveform-level hysteresis context. Evaluation on the MagNetX transient database using material-specific models for 14 ferrite materials demonstrates that PI-HNO achieves a compact trade-off between sequence accuracy and B(t)-H(t) energy consistency, with the mean and 95th percentile B(t)-H(t) energy consistency errors of 1.92% and 7.60%, respectively, using only 4777 trainable parameters per model. Ablation studies further demonstrate that the local, global, and energy-aware regularized components provide distinct contributions to transient magnetization prediction.