  Machine learning (ML) entered the field of computational micromagnetics only
recently. The main objective of these new approaches is the automatization of
solutions of parameter-dependent problems in micromagnetism such as fast
response curve estimation modeled by the Landau-Lifschitz-Gilbert (LLG)
equation. Data-driven models for the solution of time- and parameter-dependent
partial differential equations require high dimensional training
data-structures. ML in this case is by no means a straight-forward trivial
task, it needs algorithmic and mathematical innovation. Our work introduces
theoretical and computational conceptions of certain kernel and neural network
based dimensionality reduction approaches for efficient prediction of solutions
via the notion of low-dimensional feature space integration. We introduce
efficient treatment of kernel ridge regression and kernel principal component
analysis via low-rank approximation. A second line follows neural network (NN)
autoencoders as nonlinear data-dependent dimensional reduction for the training
data with focus on accurate latent space variable description suitable for a
feature space integration scheme. We verify and compare numerically by means of
a NIST standard problem. The low-rank kernel method approach is fast and
surprisingly accurate, while the NN scheme can even exceed this level of
accuracy at the expense of significant higher costs.
