Using neural networks for approximating functions and equations

• Main Author: Li, Yongming
• Other Authors: Hoang Viet Ha
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2019
• Subjects: Science::Mathematics::Analysis; Science::Mathematics::Applied mathematics::Numerical analysis
• Online Access: https://hdl.handle.net/10356/136490
• Institution: Nanyang Technological University

In this report, we develop the approximation rates of ReLU neural networks for solutions to the elliptic two-scale problems, the stochastic parabolic initial boundary value problems, and the parametric elliptic problems. We obtain bounds on network complexities - in terms of the depth size and the n...