Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An overview on deep learning-based approximation methods for partial
  differential equations   It is one of the most challenging problems in applied mathematics to
approximatively solve high-dimensional partial differential equations (PDEs).
Recently, several deep learning-based approximation algorithms for attacking
this problem have been proposed and tested numerically on a number of examples
of high-dimensional PDEs. This has given rise to a lively field of research in
which deep learning-based methods and related Monte Carlo methods are applied
to the approximation of high-dimensional PDEs. In this article we offer an
introduction to this field of research, we review some of the main ideas of
deep learning-based approximation methods for PDEs, we revisit one of the
central mathematical results for deep neural network approximations for PDEs,
and we provide an overview of the recent literature in this area of research.

26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph