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Bibliographic Details
Main Authors: Subedi, Unique, Tewari, Ambuj
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2408.09004
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Table of Contents:
  • We study learning-theoretic foundations of operator learning, using the linear layer of the Fourier Neural Operator architecture as a model problem. First, we identify three main errors that occur during the learning process: statistical error due to finite sample size, truncation error from finite rank approximation of the operator, and discretization error from handling functional data on a finite grid of domain points. Finally, we analyze a Discrete Fourier Transform (DFT) based least squares estimator, establishing both upper and lower bounds on the aforementioned errors.