most citedCell-average based neural network method for hyperbolic and parabolic partial differential equations

9 citations · 11 across the 2 of their papers we have counts for

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math.NA2021★ 9 cited

Cell-average based neural network method for hyperbolic and parabolic partial differential equations

Changxin Qiu, Jue Yan

Motivated by finite volume scheme, a cell-average based neural network method is proposed. The method is based on the integral or weak formulation of partial differential equations…

math.NA2021★ 2 cited

Accuracy and Architecture Studies of Residual Neural Network solving Ordinary Differential Equations

Changxin Qiu, Aaron Bendickson, Joshua Kalyanapu +1

In this paper we consider utilizing a residual neural network (ResNet) to solve ordinary differential equations. Stochastic gradient descent method is applied to obtain the optimal…