1 citations · 1 across the 10 of their papers we have counts for
10 papers
A Family of Even-Order Central-Upwind WENO Schemes with Averaged Downwind and Novel Global Smoothness Indicators
Jiaxi Gu, Bao-Shan Wang, Wai Sun Don +1
We propose a simple yet effective local smoothness indicator for the downwind stencil in central-upwind weighted essentially non-oscillatory (WENO) schemes of even order for hyperb…
A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
Seungwan Han, Kwanghyuk Park, Jiaxi Gu +1
We propose an efficient and generalizable physics-informed neural network (PINN) framework for computing traveling wave solutions of -dimensional reaction-diffusion equations wi…
Conservative approximation-based feedforward neural network for WENO schemes
Kwanghyuk Park, Jiaxi Gu, Jae-Hun Jung
In this work, we present the feedforward neural network based on the conservative approximation to the derivative from point values, for the weighted essentially non-oscillatory (W…
JS-type and Z-type weights for fourth-order central-upwind weighted essentially non-oscillatory schemes
Jiaxi Gu, Xinjuan Chen, Kwanghyuk Park +1
The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the d…
Neural network Approximations for Reaction-Diffusion Equations -- Homogeneous Neumann Boundary Conditions and Long-time Integrations
Eddel Elí Ojeda Avilés, Jae-Hun Jung, Daniel Olmos Liceaga
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available an…
A Numerical Study of WENO Approximations to Sharp Propagating Fronts for Reaction-Diffusion Systems
Jiaxi Gu, Daniel Olmos-Liceaga, Jae-Hun Jung
Many reaction-diffusion systems in various applications exhibit traveling wave solutions that evolve on multiple spatio-temporal scales. These traveling wave solutions are crucial…
A third-order finite difference weighted essentially non-oscillatory scheme with shallow neural network
Kwanghyuk Park, Xinjuan Chen, Dongjin Lee +2
In this paper, we introduce the finite difference weighted essentially non-oscillatory (WENO) scheme based on the neural network for hyperbolic conservation laws. We employ the sup…
Stratified Sampling Algorithms for Machine Learning Methods in Solving Two-scale Partial Differential Equations
Eddel Elí Ojeda Avilés, Daniel Olmos-Liceaga, Jae-Hun Jung
Partial differential equations (PDEs) with multiple scales or those defined over sufficiently large domains arise in various areas of science and engineering and often present prob…
Explicit radial basis function Runge-Kutta methods
Jiaxi Gu, Xinjuan Chen, Jae-Hun Jung
The aim of this paper is to design the explicit radial basis function (RBF) Runge-Kutta methods for the initial value problem. We construct the two-, three- and four-stage RBF Rung…
A spatial-temporal weight analysis and novel nonlinear weights of weighted essentially non-oscillatory schemes for hyperbolic conservation laws
Xinjuan Chen, Jiaxi Gu, Jae-Hun Jung
In this paper we analyze the weighted essentially non-oscillatory (WENO) schemes in the finite volume framework by examining the first step of the explicit third-order total variat…