Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep Multigrid: learning prolongation and restriction matrices   This paper proposes the method to optimize restriction and prolongation
operators in the two-grid method. The proposed method is straightforwardly
extended to the geometric multigrid method (GMM). GMM is used in solving
discretized partial differential equation (PDE) and based on the restriction
and prolongation operators. The operators are crucial for fast convergence of
GMM, but they are unknown. To find them we propose a reformulation of the
two-grid method in terms of a deep neural network with a specific architecture.
This architecture is based on the idea that every operation in the two-grid
method can be considered as a layer of a deep neural network. The parameters of
layers correspond to the restriction and prolongation operators. Therefore, we
state an optimization problem with respect to these operators and get optimal
ones through backpropagation approach. To illustrate the performance of the
proposed approach, we carry out experiments on the discretized Laplace
equation, Helmholtz equation and singularly perturbed convection-diffusion
equation and demonstrate that proposed approach gives operators, which lead to
faster convergence.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th