Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics
- Author(s)
- Lukas Exl, Norbert J. Mauser, Thomas Schrefl, Dieter Suess
- 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.
- Organisation(s)
- Department of Geology, Department of Mathematics, Research Platform MMM Mathematics-Magnetism-Materials, Physics of Functional Materials
- External organisation(s)
- Wolfgang Pauli Institute (WPI) Vienna, University for Continuing Education Krems
- Journal
- Communications in Nonlinear Science and Numerical Simulation
- Volume
- 84
- No. of pages
- 8
- ISSN
- 1007-5704
- DOI
- https://doi.org/10.1016/j.cnsns.2020.105205
- Publication date
- 01-2020
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101014 Numerical mathematics, 102019 Machine learning, 103018 Materials physics
- Keywords
- ASJC Scopus subject areas
- Applied Mathematics, Numerical Analysis, Modelling and Simulation
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/ede95a5c-e6f4-4ffc-ae29-0ff52ae54173