{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/115774"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/115774","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Learning aggregates and interpolation for algebraic multigrid","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms","abstract_has_math":false,"creators":["Nytko, Nicolas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["West, Matthew","Olson, Luke"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05","date_published":"2022-05","updated_at":"2026-07-22T22:24:55Z","subjects":["algebraic multigrid","smoothed aggregation","aggregation","interpolation","graphnet","graph network","machine learning","learning multigrid","evolutionary","genetic algorithm"],"languages":["en","eng"],"rights":["Copyright 2022 Nicolas Nytko"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/115774","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["West, Matthew","Olson, Luke"]},{"key":"dc:creator","label":"Author","values":["Nytko, Nicolas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-05","2022-04-26"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["algebraic multigrid","smoothed aggregation","aggregation","interpolation","graphnet","graph network","machine learning","learning multigrid","evolutionary","genetic algorithm"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Nicolas Nytko"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/115774"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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","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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Learning aggregates and interpolation for algebraic multigrid"]}]}],"canonical_facts":{"dc:contributor":["West, Matthew","Olson, Luke"],"dc:creator":["Nytko, Nicolas"],"dc:date":["2022-05","2022-04-26"],"dc:description":["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","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."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/115774"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Nicolas Nytko"],"dc:subject":["algebraic multigrid","smoothed aggregation","aggregation","interpolation","graphnet","graph network","machine learning","learning multigrid","evolutionary","genetic algorithm"],"dc:title":["Learning aggregates and interpolation for algebraic multigrid"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Computer Science"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:55Z"}