Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics
Abstract
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven approach is based on nonlinear model order reduction by use of kernel methods for unsupervised learning, yielding a predictor for the magnetization dynamics without any need for field evaluations after a data generation and training phase as precomputation. Magnetization states from simulated micromagnetic dynamics associated with different external fields are used as training data to learn a low-dimensional representation in so-called feature space and a map that predicts the time-evolution in reduced space. Remarkably, only two degrees of freedom in feature space were enough to describe the nonlinear dynamics of a thin-film element. The approach has no restrictions on the spatial discretization and might be useful for fast determination of the response to an external field.
Cite
@article{arxiv.1904.04215,
title = {Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics},
author = {Lukas Exl and Norbert J. Mauser and Thomas Schrefl and Dieter Suess},
journal= {arXiv preprint arXiv:1904.04215},
year = {2021}
}