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 straightforward trivial task; it needs algorithmic and mathematical innovation. Our work introduces theoretical and computational conceptions of the certain kernel and neural network (NN)-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. The second line follows NN autoencoders as a nonlinear data-dependent dimensional reduction for the training data with a 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 significantly higher costs.