Learning aggregates and interpolation for algebraic multigrid
Nytko, Nicolas
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https://hdl.handle.net/2142/115774
Description
Title
Learning aggregates and interpolation for algebraic multigrid
Author(s)
Nytko, Nicolas
Issue Date
2022-04-26
Director of Research (if dissertation) or Advisor (if thesis)
West, Matthew
Olson, Luke
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
algebraic multigrid
smoothed aggregation
aggregation
interpolation
graphnet
graph network
machine learning
learning multigrid
evolutionary
genetic algorithm
Language
eng
Abstract
Algebraic multigrid solvers are among the quickest for finding solutions to large, sparse linear systems of equations such as those arising from the discretization of partial differential equations (PDEs). Their implementation, however, often relies on constructing a coarse grid and transfer operators through the use of heuristics or other approximations; overall convergence depends on a judicious selection of parameters. In this thesis, we evaluate the use of neural networks to select such a coarse grid and transfer operators for isotropic and anisotropic diffusion problems. We show how graph neural networks can be used to output a tentative set of node groupings, followed by interpolation construction analogous to smoothed-aggregation multigrid. Difficulties in training such neural networks due to the lack of gradient information is addressed through the use of genetic evolution strategies. Finally, performance of the learned multigrid solver is compared to off-the-shelf methods from established algebraic multigrid packages.
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