  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.
