中国海洋大学学报（自然科学版）2024，Vol.54Issue(1)：138-143,164,7.DOI:10.16441/j.cnki.hdxb.20220422
基于图卷积的一维平流方程空间离散化数值求解加速方法
Accelerated Numerical Method for Discretization of One-Dimensional Advection Equations Based on Graph Convolution
摘要
Abstract
An accelerated numerical solution method of spatial discretization of partial differential equa-tions based on graph convolution neural network is proposed.This method is applied to the study of sol-ving one-dimensional advection equations,realizing the accelerated solution of one-dimensional advection equations.The authors designed a one-dimensional advection equation space discretization neural net-work model(GCPNN)based on graph convolution.Under the guidance of physical prior knowledge,it modeled the acceleration scheme of one-dimensional advection equation space discretization based on graph model using spatial graph structure characteristics.In the process of building graph structure rela-tionships,adjacency matrix was established based on physical prior knowledge,and global information was fused using adjacency matrix.Thus,the accelerated solution of one-dimensional advection equations was achieved.Through design comparison experiments and ablation experiments,the advantages of GCPNN based solvers in solving accuracy and computational cost compared to baseline solvers and CNN solvers were verified,and the effectiveness of incorporating physical prior knowledge guidance and global information fusion was also verified.关键词
一维平流方程/数值求解加速/图卷积/空间离散化Key words
one-dimensional advection equation/numerical solution acceleration/graph convolution/spatial discretization分类
数理科学引用本文复制引用
时津津,宋宁,田浩,聂婕,魏志强..基于图卷积的一维平流方程空间离散化数值求解加速方法[J].中国海洋大学学报（自然科学版）,2024,54(1):138-143,164,7.基金项目
国家重点研究发展计划项目(2020YFB1711700) （2020YFB1711700）
中央高校基本科研业务费专项资金项目(202042008) （202042008）
国家自然科学基金项目(62172376,62072418) （62172376,62072418）
山东省重大科技创新工程项目(2019JZZY020705)资助 Supported by the National Key Research and Development Program of China(2020YFB1711700) （2019JZZY020705）
the Fundamental Research Funds for the Central Universities(202042008) （202042008）
the National Natural Science Foundation of China(62172376,62072418) （62172376,62072418）
the Major Scientific and Technological Innovation Project of Shandong(2019JZZY020705) （2019JZZY020705）
