Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning time-stepping by nonlinear dimensionality reduction to predict
  magnetization dynamics   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.

8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph