60 citations · 202 across the 22 of their papers we have counts for
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math.NA2021★ 3 cited
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…
math.NA2021★ 11 cited
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…