基于PINNs的圣维南方程组数据同化方法  

Data assimilation method of Saint-Venant equations based on PINNs

作　　者：方卫华[1,2] 徐孟启 FANG Weihua;XU Mengqi(Nanjing Research Institute of Hydrology and Water Automation,Ministry of Water Resources,Nanjing 210012,China;Key Laboratory of Flood and Drought Hazard Control,Ministry of Water Resources,Nanjing 210029,China;College of Computer and Information,Hohai University,Nanjing 211100,China)

机构地区：[1]水利部南京水利水文自动化研究所,江苏南京210012 [2]水利部水旱灾害防御重点实验室,江苏南京210029 [3]河海大学计算机与信息学院,江苏南京211100

出　　处：《水资源保护》2023年第3期24-31,64,共9页Water Resources Protection

基　　金：江苏省水利科技项目(2021073,2020024);应急管理部防汛抢险急需技术装备揭榜攻关项目(YJBA0821002)。

摘　　要：为提高河道水位流量数据同化的智能化水平,基于物理信息神经网络(PINNs)提出了圣维南方程组的数据同化方法。采用双输出网络结构解决双输出方程组的同化问题,以模拟的实测数据作为边界条件和初始条件,通过消融试验验证网络中加入时空映射缩放和平衡权重系数对同化模型的有效性,以及所提出同化方法在部分测值缺失情况下的鲁棒性。结果表明,一维非恒定流圣维南方程组的数据同化结果与Preissmann四点隐式差分法结果一致,且随着同化断面数量的增加,所获得的同化精度也稳步提升;基于PINNs的圣维南方程组数据同化方法有效,对非恒定流模拟具有较强的适应性。In order to improve the intelligent level of river water level and flow data assimilation,a data assimilation method of Saint-Venant equations was proposed based on physics-informed neural networks(PINNs).The dual-output network structure was used to solve the assimilation problem of the dual-output equations and the simulated measured data were used as the boundary conditions and initial conditions.The ablation experiments were carried out to verify the effectiveness of the assimilation model by adding the spatio-temporal mapping scaling and the balance weight coefficient in the network,and the robustness of the proposed assimilation method in the absence of some measured values.The results show that the data assimilation results of the one-dimensional unsteady Saint-Venant equations are consistent with the results of the Preissmann four point implicit difference method,and the assimilation accuracy is also steadily improved with the increase of the number of assimilation sections.The data assimilation method of Saint-Venant equations based on PINNs is effective and has strong adaptability to unsteady flow simulation.

关 键 词：圣维南方程组 物理信息神经网络 Preissmann四点隐式差分法 数据同化 

分 类 号：TV91[水利工程—水利水电工程]