Hysteresis is a ubiquitous phenomenon in magnetic materials; its modeling and identification are crucial for understanding and optimizing the behavior of electrical machines. Such machines often operate under uncertain conditions, necessitating modeling methods that can generalize across unobserved scenarios. Traditional recurrent neural architectures struggle to generalize hysteresis patterns beyond their training domains. This paper mitigates the generalization challenge by introducing a physics-aware recurrent neural network approach to model and generalize the hysteresis manifesting in sequentiality and history-dependence. The proposed method leverages ordinary differential equations (ODEs) governing the phenomenological hysteresis models to update hidden recurrent states. The effectiveness of the proposed method is evaluated by predicting generalized scenarios, including first-order reversal curves and minor loops. The results demonstrate robust generalization to previously untrained regions, even with noisy data, an essential feature that hysteresis models must have. The results highlight the advantages of integrating physics-based ODEs into recurrent architectures, including superior performance over traditional methods in capturing the complex, nonlinear hysteresis behaviors in magnetic materials.

Nonlinear hysteresis modeling is essential for estimating, controlling, and characterizing the behavior of piezoelectric material-based devices. However, current deep-learning approaches face challenges in generalizing effectively to previously unseen voltage profiles. This Letter tackles the limitation of generalization by introducing the notion of neural operators for modeling the nonlinear constitutive laws governing inverse piezoelectric hysteresis, specifically focusing on the relationship between voltage inputs and displacement responses. The study utilizes two neural operators—Fourier neural operator and the deep operator network—to predict material responses to unseen voltage profiles that are not part of the training data. Numerical experiments, including butterfly-shaped hysteresis curves, show that in accuracy and generalization to unseen voltage profiles, neural operators outperform traditional recurrent neural network-based models, including conventional gated networks. The findings highlight the potential of neural operators for modeling hysteresis in piezoelectric materials, offering advantages over existing methods in varying voltage scenarios.