Spectral Neural Operators
In recent works, the authors introduced a neural operator: a special type of neural networks that can approximate maps between infinite-dimensional spaces. Using numerical and analytical techniques, we will highlight the peculiarities of the training and evaluation of these operators. In particular,...
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Published in | Doklady. Mathematics Vol. 108; no. Suppl 2; pp. S226 - S232 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Moscow
Pleiades Publishing
01.12.2023
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | In recent works, the authors introduced a neural operator: a special type of neural networks that can approximate maps between infinite-dimensional spaces. Using numerical and analytical techniques, we will highlight the peculiarities of the training and evaluation of these operators. In particular, we will show that, for a broad class of neural operators based on integral transforms, a systematic bias is inevitable, owning to aliasing errors. To avoid this bias, we introduce
spectral neural operators
based on explicit discretization of the domain and the codomain. Although discretization deteriorates the approximation properties, numerical experiments show that the accuracy of spectral neural operators is often superior to the one of neural operators defined on infinite-dimensional Banach spaces. |
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ISSN: | 1064-5624 1531-8362 |
DOI: | 10.1134/S1064562423701107 |