78 citations · 98 across the 6 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★ 9 cited
A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations
Mustafa E. Danis, Jue Yan
We propose a new formula for the nonlinear viscous numerical flux and extend the direct discontinuous Galerkin method with interface correction (DDGIC) of Liu and Yan (H. Liu, J. Y…
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…