Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exploratory study on machine learning to couple numerical solutions
  of partial differential equations   As further progress in the accurate and efficient computation of coupled
partial differential equations (PDEs) becomes increasingly difficult, it has
become highly desired to develop new methods for such computation. In deviation
from conventional approaches, this short communication paper explores a
computational paradigm that couples numerical solutions of PDEs via
machine-learning (ML) based methods, together with a preliminary study on the
paradigm. Particularly, it solves PDEs in subdomains as in a conventional
approach but develops and trains artificial neural networks (ANN) to couple the
PDEs' solutions at their interfaces, leading to solutions to the PDEs in the
whole domains. The concepts and algorithms for the ML coupling are discussed
using coupled Poisson equations and coupled advection-diffusion equations.
Preliminary numerical examples illustrate the feasibility and performance of
the ML coupling. Although preliminary, the results of this exploratory study
indicate that the ML paradigm is promising and deserves further research.

36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol