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 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 …

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 …

Approximation accuracy and convergence behavior are essential required properties for the
computed numerical solution of differential equations. These requirements restrict the …

Green's function characterizes a partial differential equation (PDE) and maps its solution in
the entire domain as integrals. Finding the analytical form of Green's function is a non-trivial …

Numerical simulation is dominant in solving partial differential equations (PDEs), but
balancing fine-grained grids with low computational costs is challenging. Recently, solving …

This paper proposes a deep-learning-based method for recovering a signed distance
function (SDF) of a given hypersurface represented by an implicit level set function. Using …

Learning high order non-oscillatory polynomial approximation procedures which form the
backbone of high order numerical solution of partial differential equations is challenging …

In this paper, we investigate residual neural network (ResNet) method to solve ordinary
differential equations. We verify the accuracy order of ResNet ODE solver matches the …