5 papers
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…
Schwartz duality for singularly perturbed nonlinear differential equations with Chebyshev spectral method
Eunwoo Heo, Kwanghyuk Park, Jae-Hun Jung
Singularly perturbed differential equations with a Dirac delta function yield discontinuous solutions. Therefore, careful consideration is required when using numerical methods to…
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…