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

doi:10.1088/1674-1056/ac9cb9

中国物理B ›› 2023, Vol. 32 ›› Issue (4): 40207-040207.doi: 10.1088/1674-1056/ac9cb9

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

Keyi Peng(彭珂依)^1,†, Jing Yue(岳靖)^2,‡, Wen Zhang(张文)^2,§, and Jian Li(李剑)^1,¶

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

收稿日期:2022-07-06 修回日期:2022-10-08 接受日期:2022-10-21 出版日期:2023-03-10 发布日期:2023-03-17
通讯作者: Keyi Peng, Jing Yue, Wen Zhang, Jian Li E-mail:keyi_2000@163.com;yjing1995@163.com;zw15290229577@163.com;jianli@sust.edu.cn
基金资助:
Project supported in part by the National Natural Science Foundation of China (Grant No. 11771259), Shaanxi Provincial Joint Laboratory of Artificial Intelligence (Grant No. 2022JCSYS05), Innovative Team Project of Shaanxi Provincial Department of Education (Grant No. 21JP013), and Shaanxi Provincial Social Science Fund Annual Project (Grant No. 2022D332).

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

Keyi Peng(彭珂依)^1,†, Jing Yue(岳靖)^2,‡, Wen Zhang(张文)^2,§, and Jian Li(李剑)^1,¶

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

Received:2022-07-06 Revised:2022-10-08 Accepted:2022-10-21 Online:2023-03-10 Published:2023-03-17
Contact: Keyi Peng, Jing Yue, Wen Zhang, Jian Li E-mail:keyi_2000@163.com;yjing1995@163.com;zw15290229577@163.com;jianli@sust.edu.cn
Supported by:
Project supported in part by the National Natural Science Foundation of China (Grant No. 11771259), Shaanxi Provincial Joint Laboratory of Artificial Intelligence (Grant No. 2022JCSYS05), Innovative Team Project of Shaanxi Provincial Department of Education (Grant No. 21JP013), and Shaanxi Provincial Social Science Fund Annual Project (Grant No. 2022D332).

摘要/Abstract

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

Abstract: 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.

Key words: physics-informed neural networks, the unsteady Oseen equation, convergence, small sample learning

中图分类号: (Partial differential equations)

02.30.Jr

02.60.Cb (Numerical simulation; solution of equations) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

Keyi Peng(彭珂依), Jing Yue(岳靖), Wen Zhang(张文), and Jian Li(李剑). Meshfree-based physics-informed neural networks for the unsteady Oseen equations[J]. 中国物理B, 2023, 32(4): 40207-040207.

Keyi Peng(彭珂依), Jing Yue(岳靖), Wen Zhang(张文), and Jian Li(李剑). Meshfree-based physics-informed neural networks for the unsteady Oseen equations[J]. Chin. Phys. B, 2023, 32(4): 40207-040207.

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

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

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