Using deep neural networks to solve PDEs has attracted a lot of attentions recently.
However, why the deep learning method works is falling far behind its empirical success. In …

In this paper, a new modification of the weighted essentially non-oscillatory (WENO) method
for solving nonlinear degenerate parabolic equations is developed using deep learning …

In this work, we present a novel higher-order smooth artificial viscosity method for the
discontinuous Galerkin spectral element method and related high order methods. A neural …

In this paper, we develop the cell-average based neural network (CANN) method to solve
third order and fifth order Korteweg-de Vries (KdV) type equations. The CANN method is …

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 …

In this paper, we develop cell-average-based neural network (CANN) method to
approximate solutions of nonlinear Cahn–Hilliard equation and Camassa–Holm equation …

Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport
equations with many advantages and have been widely deployed in the fields of …

This paper develops a Multilayer Perceptron (MLP) smoothness detector for the hybrid
WENO scheme. Since the MLP detector contains nonlinear activation functions and large …

The discontinuous Galerkin (DG) method is widely used in numerical solution of partial
differential equations, especially for hyperbolic equations. However, for problems containing …

For strong shock waves in solutions of steady-state Euler equations, the high-order shock
capturing schemes usually suffer from the difficulty of convergence of residue close to …