# Neural oscillators for magnetic hysteresis modeling

arXiv: https://arxiv.org/abs/2308.12002 · HTML: https://mlsanity.com/paper/2308.12002/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 23 Aug 2023.

## Builds on (most cited first, 12 of 12)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks](https://mlsanity.com/paper/1902.09689/) (2019)
- [Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies](https://mlsanity.com/paper/2010.00951/) (2020)
- [UnICORNN: A recurrent model for learning very long time dependencies](https://mlsanity.com/paper/2103.05487/) (2021)
- [Long Expressive Memory for Sequence Modeling](https://mlsanity.com/paper/2110.04744/) (2021)
- [Neural Oscillators are Universal](https://mlsanity.com/paper/2305.08753/) (2023)
- [Stateful ODE-Nets using Basis Function Expansions](https://mlsanity.com/paper/2106.10820/) (2021)
- [Neural oscillators for generalization of physics-informed machine learning](https://mlsanity.com/paper/2308.08989/) (2023)
- [A local basis approximation approach for nonlinear parametric model order reduction](https://mlsanity.com/paper/2003.07716/) (2020)
- [Discovery of sparse hysteresis models for piezoelectric materials](https://mlsanity.com/paper/2302.05313/) (2023)

## Built on by (most cited first, 1 of 1)

- [Magnetic Hysteresis Modeling with Neural Operators](https://mlsanity.com/paper/2407.03261/) (2024)

## Abstract (arXiv)

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.