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.

翻译：磁滞建模对于理解磁性器件行为、实现优化设计至关重要。迄今为止，用于建模磁滞的深度学习方法在泛化至新型输入磁场时面临挑战。本文通过提出神经算子来应对这一泛化挑战，该算子通过学习磁场间的映射关系来建模呈现磁滞特性的本构关系。具体而言，我们采用三种神经算子——深度算子网络、傅里叶神经算子与小波神经算子——来预测新型一阶反转曲线与次回线，其中“新型”指这些曲线未用于模型训练。此外，本文提出一种率无关傅里叶神经算子，用于预测与训练时采样率不同的材料响应，以纳入磁滞的率无关特性。数值实验表明，神经算子能有效建模磁滞现象，在多项指标上优于传统神经循环方法，并能泛化至新型磁场。研究结果凸显了使用神经算子在变化磁场条件下建模磁滞的优势，强调了其在基于磁性材料的器件表征中的重要性。本文相关代码位于 github.com/chandratue/magnetic_hysteresis_neural_operator。