Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics
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.
- Publication:
-
Communications in Nonlinear Science and Numerical Simulations
- Pub Date:
- May 2020
- DOI:
- 10.1016/j.cnsns.2020.105205
- arXiv:
- arXiv:1904.04215
- Bibcode:
- 2020CNSNS..8405205E
- Keywords:
-
- Nonlinear model order reduction;
- Kernel principal component analysis;
- Kernelization;
- Machine learning;
- Micromagnetics;
- Physics - Computational Physics;
- Condensed Matter - Materials Science;
- 37M05;
- 62P35;
- 65Z05
- E-Print:
- Commun Nonlinear Sci Numer Simul 84 (2020), 105205