# Dynamic hysteresis model of grain-oriented ferromagnetic material using neural operators

arXiv: https://arxiv.org/abs/2504.04863 · HTML: https://mlsanity.com/paper/2504.04863/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2025.

## Built on by (most cited first, 2 of 2)

- [Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems](https://mlsanity.com/paper/2505.24578/) (2025)
- [Accounting for Hysteresis and Eddy Currents in Finite Element Simulations of Ferromagnetic Laminated Cores using a Recurrent Neural Network](https://mlsanity.com/paper/2607.14321/) (2026)

## Abstract (arXiv)

Accurately capturing the behavior of grain-oriented (GO) ferromagnetic materials is crucial for modeling the electromagnetic devices. In this paper, neural operator models, including Fourier neural operator (FNO), U-net combined FNO (U-FNO) and Deep operator network (DeepONet) are used to approximate the dynamic hysteresis models of GO steel. Furthermore, two types of data augmentation strategies including cyclic rolling augmentation and Gaussian data augmentation (GDA) are implemented to enhance the learning ability of models. With the inclusion of these augmentation techniques, the optimized models account for not only the peak values of the magnetic flux density but also the effects of different frequencies and phase shifts. The accuracy of all models is assessed using the L2-norm of the test data and the mean relative error (MRE) of calculated core losses. Each model performs well in different scenarios, but FNO consistently achieves the best performance across all cases.