60 citations · 202 across the 22 of their papers we have counts for
4 papers · 1 filter
Entropy-based convergence rates of greedy algorithms
Yuwen Li, Jonathan Siegel
We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard…
Greedy Training Algorithms for Neural Networks and Applications to PDEs
Jonathan W. Siegel, Qingguo Hong, Xianlin Jin +2
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engi…
A Priori Analysis of Stable Neural Network Solutions to Numerical PDEs
Qingguo Hong, Jonathan W. Siegel, Jinchao Xu
Methods for solving PDEs using neural networks have recently become a very important topic. We provide an a priori error analysis for such methods which is based on the $\mathcal{K…
High-Order Approximation Rates for Shallow Neural Networks with Cosine and ReLU Activation Functions
Jonathan W. Siegel, Jinchao Xu
We study the approximation properties of shallow neural networks with an activation function which is a power of the rectified linear unit. Specifically, we consider the dependence…