4 papers
Layer-wise Geometric Approximation Rates for Deep Networks
Shijun Zhang, Zuowei Shen, Yuesheng Xu
Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for…
The Adaptive Solution of High-Frequency Helmholtz Equations via Multi-Grade Deep Learning
Peiyao Zhao, Rui Wang, Tingting Wu +1
The Helmholtz equation is fundamental for modeling wave propagation in acoustics, electromagnetics, and geophysics; however, high-frequency regimes remain notoriously difficult due…
Adaptive Multi-Grade Deep Learning for Highly Oscillatory Fredholm Integral Equations of the Second Kind
Jie Jiang, Yuesheng Xu
This paper studies the use of Multi-Grade Deep Learning (MGDL) for solving highly oscillatory Fredholm integral equations of the second kind. We provide rigorous error analyses of…
Deep Neural Network Solutions for Oscillatory Fredholm Integral Equations
Jie Jiang, Yuesheng Xu
We studied the use of deep neural networks (DNNs) in the numerical solution of the oscillatory Fredholm integral equation of the second kind. It is known that the solution of the e…