Approximation of functions from Korobov spaces by deep convolutional neural networks

• Published in: Advances in computational mathematics Vol. 48; no. 6
• Main Authors: Mao, Tong, Zhou, Ding-Xuan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2022; Springer Nature B.V
• Subjects: Approximation; Artificial neural networks; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Mathematical analysis; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Visualization; Deep convolutional neural networks; Curse of dimensionality; Korobov spaces; 68T07; 41A25; Machine learning

The efficiency of deep convolutional neural networks (DCNNs) has been demonstrated empirically in many practical applications. In this paper, we establish a theory for approximating functions from Korobov spaces by DCNNs. It verifies rigorously the efficiency of DCNNs in approximating functions of m...