2026-09-19T19:03:20Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/115774 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

West, Matthew Olson, Luke 2022-05 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms The student, Nicolas Nytko, accepted the attached license on 2022-04-25 at 16:50. The student, Nicolas Nytko, submitted this Thesis for approval on 2022-04-25 at 16:57. This Thesis was approved for publication on 2022-04-26 at 17:09. DSpace SAF Submission Ingestion Package generated from Vireo submission #17663 on 2022-11-11 at 17:38:02 Learning aggregates and interpolation for algebraic multigrid Nytko, Nicolas 2022-04-26 algebraic multigrid smoothed aggregation aggregation interpolation graphnet graph network machine learning learning multigrid evolutionary genetic algorithm 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. Thesis eng https://hdl.handle.net/2142/115774 Copyright 2022 Nicolas Nytko M.S. Thesis Computer Science University of Illinois at Urbana-Champaign Computer Science