一种风向监督双流神经网络--以一维Burgers方程求解为例  

A Dual-Stream Neural Network Supervised by Wind Direction for One-Dimensional Burgers Equation

作　　者：耿浩冉 田浩 王成龙 宋宁 魏志强[1] 冯毅雄[3] 郭景任 聂婕[1] Geng Haoran;Tian Hao;Wang Chenglong;Song Ning;Wei Zhiqiang;Feng Yixiong;Guo Jingren;Nie Jie(Faculty of Information Science and Engineering,Ocean University of China,Qingdao 266100,China;School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China;School of Mechanical Engineering,Zhejiang University,Hangzhou 310058,China;Shenzhen Zhongguang Nuclear Engineering Design Corporation Limited,Shen-zhen 519000,China)

机构地区：[1]中国海洋大学信息科学与工程学部,山东青岛266100 [2]中国海洋大学数学科学学院,山东青岛266100 [3]浙江大学机械工程学院,浙江杭州310058 [4]深圳中广核工程设计有限公司,广东深圳519000

出　　处：《中国海洋大学学报（自然科学版）》2024年第2期134-141,共8页Periodical of Ocean University of China

基　　金：国家重点研究发展计划项目(2020YFB1711700);中央高校基本科研业务费专项资金项目(202042008);国家自然科学基金项目(62172376,62072418);山东省重大科技创新工程项目(2019JZZY020705)资助。

摘　　要：针对一维Burgers方程下单一建模方式难以充分考虑不同阶段风向对系数的影响比重,无法有效获得各节点间的关联信息的问题,本文提出了一种风向监督双流神经网络分别预测上下风向的有限差分系数。同时设计了一种风向判断模块,实现了对预测得到有限差分系数的权重融合。通过风向监督双流神经网络,并结合先验知识对学得的系数分配一定的权重,以突出上下风向对预测结果的不同影响,可以有效实现对不同风向上的点分别进行预测,使得空间结构特征信息挖掘更加充分,从而提高差分系数预测的精度。在比传统数值求解方法网格分辨率粗4~8倍的同时,提高了谷歌团队工作的精度,以此提高了计算的速度。Aiming at the problem that the single modeling method under the one-dimensional Burgers equation is difficult to fully consider the influence of wind direction on the coefficient at different stages,and cannot effectively obtain the relevant information between nodes.A wind direction supervised two-stream neural network is proposed to predict the finite difference coefficients of up and down wind directions separately.At the same time,a wind direction judgment module is designed to realize the weight fusion of the predicted finite difference coefficients.The two-stream neural network is supervised by the wind direction,combined with the prior knowledge to assign a certain weight to the learned coefficients,so as to highlight the different influences of the upper and lower wind directions on the prediction results,and can effectively realize the prediction of points in different wind directions,making the spatial structure characteristics Information mining is more sufficient,thereby improving the accuracy of differential coefficient prediction.While the grid resolution is 4 to 8 times thicker than the traditional numerical solution method,it improves the accuracy of the work of the Google team,thereby increasing the calculation speed.

关 键 词：风向监督双流神经网络 BURGERS方程 机器学习 迎风格式 数据驱动离散化 

分 类 号：O242.1[理学—计算数学]