  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.
