52 citations · 103 across the 12 of their papers we have counts for
5 papers · 1 filter
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Chenguang Duan, Yuling Jiao, Yanming Lai +3
Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in norm for dee…
A rate of convergence of Physics Informed Neural Networks for the linear second order elliptic PDEs
Yuling Jiao, Yanming Lai, Dingwei Li +4
In recent years, physical informed neural networks (PINNs) have been shown to be a powerful tool for solving PDEs empirically. However, numerical analysis of PINNs is still missing…
Error Analysis of Deep Ritz Methods for Elliptic Equations
Yuling Jiao, Yanming Lai, Yisu Lo +2
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In thi…
Convergence Rate Analysis for Deep Ritz Method
Chenguang Duan, Yuling Jiao, Yanming Lai +2
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In thi…
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class
Yuling Jiao, Yanming Lai, Xiliang Lu +3
In this paper, we construct neural networks with ReLU, sine and as activation functions. For general continuous defined on with continuity modulus ,…