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

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

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.

Department of Mathematics, Physics of Functional Materials
External organisation(s)
Wolfgang Pauli Institute (WPI) Vienna
Publication date
Austrian Fields of Science 2012
Numerical mathematics, Machine learning, Materials physics
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