浙江大学学报（理学版）2024，Vol.51Issue(6)：724-731,8.DOI:10.3785/j.issn.1008-9497.2024.06.008
求解双曲型方程的半离散卷积神经网络算法
A semi discrete convolutional neural network algorithm for solving hyperbolic equations
摘要
Abstract
The existence of discontinuous solutions of the hyperbolic conservation laws calls for require strict numerical algorithms.Traditional low order numerical algorithms are usually easy to construct,but the resolution of the numerical results is low and depends on the grid.Machine learning methods do not rely on grids and are suitable for dealing with complex scenarios(such as high-dimensional problems),but there may be displacement or smoothing phenomena when solving discontinuous problems.By combining machine learning with traditional low order formats and leveraging their advantages,this paper adopts a low order finite volume format,and uses convolutional neural networks to optimize weight coefficients.High resolution numerical results can be obtained by solving with fewer nodes.We demonstrate the good performance of the algorithm through several numerical examples which shows that the algorithm can obtain high-resolution numerical results for both continuous and discontinuous problems without any displacement or smoothing phenomena.关键词
双曲守恒律方程/有限体积法/卷积神经网络模型Key words
hyperbolic conservation law equation/finite volume method/convolutional neural network model分类
数理科学引用本文复制引用
汪浏博,郑素佩,张蕊,封建湖..求解双曲型方程的半离散卷积神经网络算法[J].浙江大学学报（理学版）,2024,51(6):724-731,8.基金项目
国家自然科学基金资助项目(11971075) （11971075）
陕西省自然科学基础研究计划重点项目(2024JC-ZDXM-23). （2024JC-ZDXM-23）
