Magnetic Hysteresis Modeling with Neural Operators

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.

11 pages, 6 figures

References in corpus (3)

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Physics-informed neural networks for solving forward and inverse problems in complex beam systems
• In-Context Operator Learning with Data Prompts for Differential Equation Problems

Cited by in corpus (1)

• Dynamic hysteresis model of grain-oriented ferromagnetic material using neural operators