9 citations · 11 across the 3 of their papers we have counts for
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math.NA2022
A generalized framework for direct discontinuous Galerkin methods for nonlinear diffusion equations
Mustafa Engin Danis, Jue Yan
In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the nonlinear diffusion matrix is…
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…