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.

Figures (6)

• Figure 1: Deep operator network (DeepONet) architecture. The architecture consists of two separate feedforward neural networks— branch net and trunk net— whose outputs are combined using a dot product to approximate the $B$ fields.
• Figure 2: Neural architecture for Fourier neural operator (FNO) and rate-independent Fourier neural operator (RIFNO). For FNO the input $X\!:= [h_i, t_\text{sample}]$, whereas for RIFNO, $X:=h_i$. The input is passed through projection tensor ($P$) and Fourier layers and finally downscaled ($Q$) to approximate the $B$ field.
• Figure 3: Neural architecture for wavelet neural operator (WNO). The input $X\!:= [h_i, t_\text{sample}]$ is passed through projection tensor ($P$) and wavelet integral layers and finally downscaled ($Q$) to approximate the $B$ field.
• Figure 4: Performance of neural networks on predicting the first-order reversal curves. Top row: (From Left) the predictions (preds.) of the $B$ fields by DeepONet, FNO, WNO, RIFNO, LSTM, and Encoder-Decoder LSTM (EDLSTM) respectively. Middle row: (From Left) the predicted hysteresis loops (in red) compared with the reference (ref.) loops (in black) for the six methods. Bottom row: (From Left) absolute errors in predicting the FORCs for the six methods (in green).
• Figure 5: Variation of relative error with respect to different testing rates for neural operators.