Prediction of magnetization dynamics in a reduced dimensional feature space setting utilizing a low-rank kernel method

TL;DR

This paper introduces a machine learning approach using low-rank kernel methods to efficiently predict magnetization dynamics governed by the Landau-Lifschitz-Gilbert equation, significantly reducing computational complexity.

Contribution

It presents a novel low-rank kernel-based model that reduces dimensionality and accelerates prediction of micromagnetic responses to external fields.

Findings

Accurate prediction of magnetization dynamics in thin films.

Significant reduction in computational complexity.

Effective handling of large training datasets.

Abstract

We establish a machine learning model for the prediction of the magnetization dynamics as function of the external field described by the Landau-Lifschitz-Gilbert equation, the partial differential equation of motion in micromagnetism. The model allows for fast and accurate determination of the response to an external field which is illustrated by a thin-film standard problem. The data-driven method internally reduces the dimensionality of the problem by means of nonlinear model reduction for unsupervised learning. This not only makes accurate prediction of the time steps possible, but also decisively reduces complexity in the learning process where magnetization states from simulated micromagnetic dynamics associated with different external fields are used as input data. We use a truncated representation of kernel principal components to describe the states between time predictions. The method is capable of handling large training sample sets owing to a low-rank approximation of the kernel matrix and an associated low-rank extension of kernel principal component analysis and kernel ridge regression. The approach entirely shifts computations into a reduced dimensional setting breaking down the problem dimension from the thousands to the tens.