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, two prominent neural operators -- deep operator network and Fourier 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.

提出了使用神经算子对磁滞建模的方法，以解决常规神经网络方法难以推广至新输入磁场的问题；通过深度算子网络和傅里叶神经算子对新一阶反向曲线和次环进行预测，并提出了一个无速率相关的傅里叶神经算子用于在采样速率不同的情况下预测材料响应。数值实验证明，神经算子能够高效地建模磁滞，并在各个指标上优于传统的循环神经网络方法，并能够推广至新的磁场条件，强调了神经算子在表征基于磁性材料的器件中的重要性。

使用神经算子建模磁滞