Learning aggregates and interpolation for algebraic multigrid

Nytko, Nicolas

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https://hdl.handle.net/2142/115774 Copy

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

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.

Graduation Semester

2022-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Nicolas Nytko

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