{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/120438"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/120438","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Operator learning in the overparameterized regime","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","abstract_has_math":false,"creators":["Shrimali, Bhavesh"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Banerjee, Arindam"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-05","date_published":"2023-05","updated_at":"2026-07-22T22:24:57Z","subjects":["Overparameterization","Optimization","Deep Operator Networks"],"languages":["en","eng"],"rights":["Copyright 2023 Bhavesh Shrimali"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/120438","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Banerjee, Arindam"]},{"key":"dc:creator","label":"Author","values":["Shrimali, Bhavesh"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05","2023-05-01"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"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":["Overparameterization","Optimization","Deep Operator Networks"]}]},{"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 2023 Bhavesh Shrimali"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/120438"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","The student, Bhavesh Shrimali, accepted the attached license on 2023-04-28 at 13:10.","The student, Bhavesh Shrimali, submitted this Thesis for approval on 2023-04-28 at 13:14.","This Thesis was approved for publication on 2023-05-01 at 14:46.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19241 on 2023-09-01 at 17:15:19","Neural Operators that directly learn mappings between function spaces have received considerable recent attention. Deep Operator Networks (DeepONets), a popular recent class of operator networks have shown promising preliminary results in approximating solution operators of parametric partial differential equations. Despite the universal approximation guarantees there is yet no optimization convergence guarantee for DeepONets based on gradient descent (GD). In this thesis, we establish such guarantees and show that overparameterization based on wide layers provably helps. In particular, we present two types of optimization convergence analysis: first, for smooth activations, we bound the spectral norm of the Hessian of DeepONets and use the bound to show geometric convergence of GD based on restricted strong convexity (RSC); and second, for ReLU activations, we show the neural tangent kernel (NTK) of DeepONets at initialization is positive definite, which can be used with the standard NTK analysis to imply geometric convergence. Further, we present empirical results on three canonical operator learning problems: Antiderivative, DiffusionReaction equation, and Burger’s equation, and show that wider DeepONets lead to lower training loss on all the problems, thereby supporting the theoretical results"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Operator learning in the overparameterized regime"]}]}],"canonical_facts":{"dc:contributor":["Banerjee, Arindam"],"dc:creator":["Shrimali, Bhavesh"],"dc:date":["2023-05","2023-05-01"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01","The student, Bhavesh Shrimali, accepted the attached license on 2023-04-28 at 13:10.","The student, Bhavesh Shrimali, submitted this Thesis for approval on 2023-04-28 at 13:14.","This Thesis was approved for publication on 2023-05-01 at 14:46.","DSpace SAF Submission Ingestion Package generated from Vireo submission #19241 on 2023-09-01 at 17:15:19","Neural Operators that directly learn mappings between function spaces have received considerable recent attention. Deep Operator Networks (DeepONets), a popular recent class of operator networks have shown promising preliminary results in approximating solution operators of parametric partial differential equations. Despite the universal approximation guarantees there is yet no optimization convergence guarantee for DeepONets based on gradient descent (GD). In this thesis, we establish such guarantees and show that overparameterization based on wide layers provably helps. In particular, we present two types of optimization convergence analysis: first, for smooth activations, we bound the spectral norm of the Hessian of DeepONets and use the bound to show geometric convergence of GD based on restricted strong convexity (RSC); and second, for ReLU activations, we show the neural tangent kernel (NTK) of DeepONets at initialization is positive definite, which can be used with the standard NTK analysis to imply geometric convergence. Further, we present empirical results on three canonical operator learning problems: Antiderivative, DiffusionReaction equation, and Burger’s equation, and show that wider DeepONets lead to lower training loss on all the problems, thereby supporting the theoretical results"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/120438"],"dc:language":["en","eng"],"dc:rights":["Copyright 2023 Bhavesh Shrimali"],"dc:subject":["Overparameterization","Optimization","Deep Operator Networks"],"dc:title":["Operator learning in the overparameterized regime"],"dc:type":["text"],"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":"2026-07-22T22:24:57Z"}