52 citations · 141 across the 16 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…
Global Optimization via Schr{ö}dinger-F{ö}llmer Diffusion
Yin Dai, Yuling Jiao, Lican Kang +2
We study the problem of finding global minimizers of approximately via sampling from a probability distribution with density $p_σ(x)=…
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…
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 ,…