Learning aggregates and interpolation for algebraic multigrid

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Nytko, Nicolas

Contributors dc:contributor

• West, Matthew
• Olson, Luke

• algebraic multigrid
• smoothed aggregation
• aggregation
• interpolation
• graphnet
• graph network
• machine learning
• learning multigrid
• evolutionary
• genetic algorithm

Statement dc:rights

• Copyright 2022 Nicolas Nytko

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115774