基于人工神经网络的WENO重构方法
The WENO Reconstruction Based on the Artificial Neural Network
DOI: 10.12677/AAM.2020.94069, PDF,  被引量   
作者: 刘 琪：中国海洋大学数学科学学院，山东 青岛；温 晓：山东科技大学数学与系统科学学院，山东 青岛
关键词: 人工神经网络；WENO格式；非线性权重；Artificial Neural Network； WENO Scheme； Non-Linear Weights
摘要: 本文提出了一种基于人工神经网络(ANN)的WENO重构方法，用ANN来近似WENO-JS中的非线性权重，其中ANN的输入为用于五阶WENO求解的模板中的五点函数值，输出为三个子模板的光滑性指标，光滑性指标可直接转化为对应的非线性权重，用于WENO重构。数值实验表明，与WENO-JS相比，WENO-ANN能保持精度，且数值色散耗散较低。
Abstract: A method for WENO reconstruction based on the artificial neural network (ANN) is proposed, which uses the ANN to approximate the non-linear weights in WENO-JS, where the input of the ANN is the value of the five-point function in the stencil for fifth-order WENO scheme, and the output is the smoothness indicators of the three sub-stencils. The smoothness indicators can be directly converted into corresponding non-linear weights for WENO reconstruction. Numerical experiments show that, compared with the WENO-JS scheme, the WENO-ANN can maintain accuracy, the numerical dispersion and dissipation are lower.
文章引用：刘琪, 温晓. 基于人工神经网络的WENO重构方法[J]. 应用数学进展, 2020, 9(4): 574-583. https://doi.org/10.12677/AAM.2020.94069

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