Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929701703909376 |
|---|---|
| author | Subedi, Unique Tewari, Ambuj |
| author_facet | Subedi, Unique Tewari, Ambuj |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators Subedi, Unique Tewari, Ambuj Machine Learning Numerical Analysis 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. |
| title | Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2408.09004 |