Meshfree-based physics-informed neural networks for the unsteady Oseen equations  

作　　者：彭珂依 岳靖 张文 李剑 Keyi Peng;Jing Yue;Wen Zhang;Jian Li(School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi’an 710021,China;School of Electrical and Control Engineering,Shaanxi University of Science and Technology,Xi’an 710021,China)

机构地区：[1]School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi’an 710021,China [2]School of Electrical and Control Engineering,Shaanxi University of Science and Technology,Xi’an 710021,China

出　　处：《Chinese Physics B》2023年第4期151-159,共9页中国物理B（英文版）

基　　金：Project supported in part by the National Natural Science Foundation of China(Grant No.11771259);Shaanxi Provincial Joint Laboratory of Artificial Intelligence(GrantNo.2022JCSYS05);Innovative Team Project of Shaanxi Provincial Department of Education(Grant No.21JP013);Shaanxi Provincial Social Science Fund Annual Project(Grant No.2022D332)。

摘　　要：We propose the meshfree-based physics-informed neural networks for solving the unsteady Oseen equations.Firstly,based on the ideas of meshfree and small sample learning,we only randomly select a small number of spatiotemporal points to train the neural network instead of forming a mesh.Specifically,we optimize the neural network by minimizing the loss function to satisfy the differential operators,initial condition and boundary condition.Then,we prove the convergence of the loss function and the convergence of the neural network.In addition,the feasibility and effectiveness of the method are verified by the results of numerical experiments,and the theoretical derivation is verified by the relative error between the neural network solution and the analytical solution.

关 键 词：physics-informed neural networks the unsteady Oseen equation convergence small sample learning 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程] O241.82[自动化与计算机技术—控制科学与工程]