  We establish a machine learning model for the prediction of the magnetization
dynamics as function of the external field described by the
Landau-Lifschitz-Gilbert equation, the partial differential equation of motion
in micromagnetism. The model allows for fast and accurate determination of the
response to an external field which is illustrated by a thin-film standard
problem. The data-driven method internally reduces the dimensionality of the
problem by means of nonlinear model reduction for unsupervised learning. This
not only makes accurate prediction of the time steps possible, but also
decisively reduces complexity in the learning process where magnetization
states from simulated micromagnetic dynamics associated with different external
fields are used as input data. We use a truncated representation of kernel
principal components to describe the states between time predictions. The
method is capable of handling large training sample sets owing to a low-rank
approximation of the kernel matrix and an associated low-rank extension of
kernel principal component analysis and kernel ridge regression. The approach
entirely shifts computations into a reduced dimensional setting breaking down
the problem dimension from the thousands to the tens.
