Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning to Optimize Multigrid PDE Solvers   Constructing fast numerical solvers for partial differential equations (PDEs)
is crucial for many scientific disciplines. A leading technique for solving
large-scale PDEs is using multigrid methods. At the core of a multigrid solver
is the prolongation matrix, which relates between different scales of the
problem. This matrix is strongly problem-dependent, and its optimal
construction is critical to the efficiency of the solver. In practice, however,
devising multigrid algorithms for new problems often poses formidable
challenges. In this paper we propose a framework for learning multigrid
solvers. Our method learns a (single) mapping from a family of parameterized
PDEs to prolongation operators. We train a neural network once for the entire
class of PDEs, using an efficient and unsupervised loss function. Experiments
on a broad class of 2D diffusion problems demonstrate improved convergence
rates compared to the widely used Black-Box multigrid scheme, suggesting that
our method successfully learned rules for constructing prolongation matrices.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an