Magnetic Hysteresis Modeling with Neural Operators

TL;DR

This paper introduces neural operators to model magnetic hysteresis, enabling better generalization to new magnetic inputs and varying sampling rates, outperforming traditional methods.

Contribution

It proposes the use of neural operators for hysteresis modeling, including a rate-independent Fourier neural operator, to improve generalization and accuracy over existing neural recurrent approaches.

Findings

Neural operators effectively model magnetic hysteresis.

They outperform traditional neural recurrent methods.

They generalize well to novel magnetic fields and different sampling rates.

Abstract

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.