Hysteresis is a ubiquitous phenomenon in science and engineering; its modeling and identification are crucial for understanding and optimizing the behavior of various systems. We develop an ordinary differential equation-based recurrent neural network (RNN) approach to model and quantify the hysteresis, which manifests itself in sequentiality and history-dependence. Our neural oscillator, HystRNN, draws inspiration from coupled-oscillatory RNN and phenomenological hysteresis models to update the hidden states. The performance of HystRNN is evaluated to predict generalized scenarios, involving first-order reversal curves and minor loops. The findings show the ability of HystRNN to generalize its behavior to previously untrained regions, an essential feature that hysteresis models must have. This research highlights the advantage of neural oscillators over the traditional RNN-based methods in capturing complex hysteresis patterns in magnetic materials, where traditional rate-dependent methods are inadequate to capture intrinsic nonlinearity.

翻译：磁滞是科学与工程中的普遍现象，其建模与辨识对理解和优化各类系统行为至关重要。我们提出一种基于常微分方程的循环神经网络方法，用于建模和量化以序列性和历史依赖性为特征的磁滞效应。所提出的神经振子HystRNN借鉴耦合振荡循环网络与现象学磁滞模型的思想来更新隐状态。通过预测包含一阶反转曲线和次环在内的泛化场景，评估了HystRNN的性能。结果表明，HystRNN能够将行为泛化至未经训练的区域——这是磁滞模型必备的核心特性。本研究揭示了神经振子相比传统基于循环神经网络的方法在捕捉磁性材料复杂磁滞模式中的优势，而传统速率依赖型方法难以刻画其内在非线性特征。