Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics

Autor(en)

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

Abstrakt

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.

Organisation(en)

Institut für Geologie, Institut für Mathematik, Forschungsplattform MMM Mathematics-Magnetism-Materials, Physik Funktioneller Materialien

Externe Organisation(en)

Wolfgang Pauli Institute (WPI) Vienna, Universität für Weiterbildung Krems

Journal

Communications in Nonlinear Science and Numerical Simulation

Band

84

Anzahl der Seiten

8

ISSN

1007-5704

DOI

https://doi.org/10.1016/j.cnsns.2020.105205

Publikationsdatum

01-2020

Peer-reviewed

Ja

ÖFOS 2012

101014 Numerische Mathematik, 102019 Machine Learning, 103018 Materialphysik

Schlagwörter

ASJC Scopus Sachgebiete

Applied Mathematics, Numerical Analysis, Modelling and Simulation

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/ede95a5c-e6f4-4ffc-ae29-0ff52ae54173