# Magnetic Hysteresis Modeling with Neural Operators

arXiv: https://arxiv.org/abs/2407.03261 · HTML: https://mlsanity.com/paper/2407.03261/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Builds on (most cited first, 15 of 15)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs](https://mlsanity.com/paper/2006.16144/) (2020)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [Learning Operators with Coupled Attention](https://mlsanity.com/paper/2201.01032/) (2022)
- [Physics-informed neural networks for solving forward and inverse problems in complex beam systems](https://mlsanity.com/paper/2303.01055/) (2023)
- [Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses](https://mlsanity.com/paper/2401.06070/) (2024)
- [Neural oscillators for generalization of physics-informed machine learning](https://mlsanity.com/paper/2308.08989/) (2023)
- [Transfer learning for improved generalizability in causal physics-informed neural networks for beam simulations](https://mlsanity.com/paper/2311.00578/) (2023)
- [Neural oscillators for magnetic hysteresis modeling](https://mlsanity.com/paper/2308.12002/) (2023)

## Built on by (most cited first, 3 of 3)

- [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)
- [A Physics-Informed Hybrid Neural Operator for Transient Magnetization Prediction in Power Magnetics](https://mlsanity.com/paper/2608.02965/) (2026)

## Abstract (arXiv)

Hysteresis modeling is crucial to comprehend the behavior of magnetic devices, facilitating optimal designs. Hitherto, deep learning-based methods employed to model hysteresis, face challenges in generalizing to novel input magnetic fields. This paper addresses the generalization challenge by proposing neural operators for modeling constitutive laws that exhibit magnetic hysteresis by learning a mapping between magnetic fields. In particular, three neural operators-deep operator network, Fourier neural operator, and wavelet neural operator-are employed to predict novel first-order reversal curves and minor loops, where novel means they are not used to train the model. In addition, a rate-independent Fourier neural operator is proposed to predict material responses at sampling rates different from those used during training to incorporate the rate-independent characteristics of magnetic hysteresis. The presented numerical experiments demonstrate that neural operators efficiently model magnetic hysteresis, outperforming the traditional neural recurrent methods on various metrics and generalizing to novel magnetic fields. The findings emphasize the advantages of using neural operators for modeling hysteresis under varying magnetic conditions, underscoring their importance in characterizing magnetic material based devices. The codes related to this paper are at github.com/chandratue/magnetic_hysteresis_neural_operator.