2026-09-19T16:07:51Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/120438 2023-09-05 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Banerjee, Arindam 2023-05 application/pdf en text 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 Operator learning in the overparameterized regime Shrimali, Bhavesh 2023-05-01 Overparameterization Optimization Deep Operator Networks 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 Text eng https://hdl.handle.net/2142/120438 Copyright 2023 Bhavesh Shrimali M.S. Thesis Computer Science University of Illinois at Urbana-Champaign Computer Science