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

by   Lukas Exl, et al.

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.



page 9

page 10

page 16

page 17

page 20

page 24


Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation

Robust principal component analysis (RPCA) is a widely used tool for dim...

Solving for the low-rank tensor components of a scattering wave function

Atomic and molecular breakup reactions, such as multiple-ionisation, are...

Dimensionality Reduction and Wasserstein Stability for Kernel Regression

In a high-dimensional regression framework, we study consequences of the...

Learning Green's functions associated with parabolic partial differential equations

Given input-output pairs from a parabolic partial differential equation ...

Low-Rank Nonlinear Decoding of μ-ECoG from the Primary Auditory Cortex

This paper considers the problem of neural decoding from parallel neural...

Learning Representation from Neural Fisher Kernel with Low-rank Approximation

In this paper, we study the representation of neural networks from the v...

Model Order Reduction of Combustion Processes with Complex Front Dynamics

In this work we present a data driven method, used to improve mode-based...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.