数据驱动的高分辨率CCWENO-ANN算法OA

To accurately solve hyperbolic conservation laws and obtain high-resolution numerical results,this paper combined data-driven with the third-order CCWENO(Compact Central Weighted Essentially Non-Oscillatory)scheme,and proposed a data-driven CCWENO-ANN high-resolution scheme for hyperbolic conservation laws.By constructing the normalized calibration layer and sparse layer of an artificial neural network,the appropriate prior knowledge is introduced to accelerate the convergence speed.At the same time,the loss function dynamically adjusts the deviation between the outputs of the neural network and the ideal weights,and uses the supervised learning strategy to train the neural network offline on the appropriate data set to improve the performance of the neural network.By solving one-dimensional inviscid Burgers equation,one-dimensional Euler equation,two-dimensional inviscid Burgers equation and two-dimensional Euler equation,the performance of the algorithm is evaluated.The results show that the proposed CCWENO-ANN inherits the convergence of the traditional CCWENO scheme and can accurately capture shock waves and contact discontinuities,and has the advantages of robustness,low dissipation and high resolution.