  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.
