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A Multi-Scale ResNet-augmented Fourier Neural Operator Framework for High-Frequency Sequence-to-Sequence Prediction of Magnetic Hysteresis

Ziqing Guo, Xiaobing Shen, Ruth V. Sabariego

Abstract

Accurate modeling of magnetic hysteresis is essential for high-fidelity power electronics device simulations. The transient hysteresis phenomena such as the ringing effect and the minor loops are the bottleneck for the accurate hysteresis modeling and the core losses estimation. To capture the hysteresis loops with both the macro structure and the micro transient details, in this paper, we propose the multi-scale ResNet augmented Fourier Neural Operator (Res-FNO). The framework employs a hybrid input structure that combines sequential time-series data with scalar material labels through specialized feature engineering. Specifically, the time derivative of magnetic flux density ($\frac{dB}{dt}$) is incorporated as a critical physical feature to enhance the model sensitivity to high-frequency oscillations and minor loop triggers. The proposed architecture synergizes global spectral modeling with localized refinement by integrating a multi-scale ResNet path in parallel with the FNO blocks. This design allows the global operator path to capture the underlying physical evolution while the local refinement path, compensates for spectral bias and reconstructs fine-grained temporal details. Extensive experimental validation across diverse magnetic materials from 79 to Material 3C90 demonstrates the strong generalization capability of the proposed Res-FNO, proving its robust ability to model complex ringing effects and minor loops in realistic power electronic applications.

A Multi-Scale ResNet-augmented Fourier Neural Operator Framework for High-Frequency Sequence-to-Sequence Prediction of Magnetic Hysteresis

Abstract

Accurate modeling of magnetic hysteresis is essential for high-fidelity power electronics device simulations. The transient hysteresis phenomena such as the ringing effect and the minor loops are the bottleneck for the accurate hysteresis modeling and the core losses estimation. To capture the hysteresis loops with both the macro structure and the micro transient details, in this paper, we propose the multi-scale ResNet augmented Fourier Neural Operator (Res-FNO). The framework employs a hybrid input structure that combines sequential time-series data with scalar material labels through specialized feature engineering. Specifically, the time derivative of magnetic flux density () is incorporated as a critical physical feature to enhance the model sensitivity to high-frequency oscillations and minor loop triggers. The proposed architecture synergizes global spectral modeling with localized refinement by integrating a multi-scale ResNet path in parallel with the FNO blocks. This design allows the global operator path to capture the underlying physical evolution while the local refinement path, compensates for spectral bias and reconstructs fine-grained temporal details. Extensive experimental validation across diverse magnetic materials from 79 to Material 3C90 demonstrates the strong generalization capability of the proposed Res-FNO, proving its robust ability to model complex ringing effects and minor loops in realistic power electronic applications.

Paper Structure

This paper contains 19 sections, 4 equations, 13 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Problem formulation and data representation
  3. Model description
  4. Multi-input processing
  5. Res-FNO
  6. ResNet with the residual connection
  7. FNO block
  8. FNO with Resnet
  9. Feature engineering
  10. Loss function constraints
  11. Results
  12. Experimental configuration
  13. Ablation study on hybrid multi-scale Res-FNO components
  14. Influence of ResNet integrated FNO
  15. Efficacy of model inputs processing
  16. ...and 4 more sections

Figures (13)

  • Figure 1: Structure of multi-scale Res-FNO: (Left) Multi-input Processing to fuse the scalar and sequential inputs; (Right) Res-FNO with parallel FNO blocks and ResNet blocks.
  • Figure 2: Residual learning: a building block resnet2016
  • Figure 3: Structure of Res-FNO block: Up Global operator path with FNO blocks to capture underlying physical evolution; (Down) Local refinement path with ResNet blocks for multi-scale feature reconstruction.
  • Figure 4: Typical magnetic characteristics under high-frequency excitation: (Left) Temporal waveform of the magnetic induction $B(t)$; (Middle) Corresponding magnetic field strength $H(t)$ exhibiting a pronounced ringing effect; (Right) The resulting $B$-$H$ hysteresis loops, illustrating the impact of temporal oscillations on the magnetic trajectory.
  • Figure 5: NRMSE distribution analysis for different model architectures.
  • ...and 8 more figures