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Aug, 2024
学习傅里叶线性算子的误差边界
Error Bounds for Learning Fourier Linear Operators
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Unique Subedi, Ambuj Tewari
TL;DR
本研究解决了在函数空间中学习算子时存在的三种主要误差，包括统计误差、截断误差和离散化误差。通过分析基于离散傅里叶变换的最小二乘估计器，本文建立了这些误差的上下界，提供了一种新的视角来理解傅里叶神经算子的学习过程，对提高其应用效果具有潜在影响。
Abstract
We investigate the problem of
Learning Operators
between function spaces, focusing on the linear layer of the
Fourier Neural Operator
. First, we identify three main errors that occur during the learning process:
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