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

Lukas Exl, Norbert J. Mauser, Sebastian Schaffer, Thomas Schrefl, Dieter Suess

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.

Department of Mathematics, Research Platform MMM Mathematics-Magnetism-Materials, Faculty of Physics, Physics of Functional Materials
External organisation(s)
Wolfgang Pauli Institute (WPI) Vienna, Donau-Universität Krems
Journal of Computational Physics
No. of pages
Publication date
Peer reviewed
Austrian Fields of Science 2012
101014 Numerical mathematics, 103043 Computational physics, 102019 Machine learning
ASJC Scopus subject areas
Computational Mathematics, Physics and Astronomy(all), Applied Mathematics, Numerical Analysis, Computer Science Applications, Modelling and Simulation, Physics and Astronomy (miscellaneous)
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