基于神经网络改进WENO-Z重构方法

本文通过使用深度神经网络对WENO-Z格式的非线性权重进行改进，提出了一种新的WENO-Z-NN格式．新格式首先用神经网络去随机扰动有限体积系数集，然后用代表偏微分方程解的波形生成的数据，采用L2正则化来学习扰动的最优函数，最后引入测试函数并结合最小总变差和最小总偏差作为评估依据进行后处理，从而得到新的权重．一维波动方程和一维Euler方程的数值结果表明，无论是在粗网格还是在细网格，本文所提出的WENO-Z-NN格式的激波捕捉能力明显优于传统的WENO-Z和WENO-JS-NN格式．

Improved WENO-Z Reconstruction Method Based on Neural Network

In this paper, a new WENO-Z-NN scheme is proposed by improving the nonlinear weights of the WENO-Z scheme using the deep neural network. In the new WENO-Z method, we use a neural network to randomly perturb the finite volume coefficient sets, then the data generated by waveform representing the solution of partial differential equation are used to learn the perturbed optimal function by L2 regularization. Finally, we introduce a test function as the post-process by combining minimum total variation and minimum total deviation for an evaluation basis, thus getting the new weights. The numerical results of the one-dimensional wave and Euler equations show that the shock-capturing ability of the presented WENO-Z-NN scheme is significantly better than that of the traditional WENO-Z and WENO-JS-NN schemes, whether in coarse grid or fine grid.