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The coupled deep neural networks for coupling of the Stokes and Darcy-Forchheimer problems |
| Jing Yue(岳靖)1, Jian Li(李剑)1,†, Wen Zhang(张文)1, and Zhangxin Chen(陈掌星)2,3 |
1 School of Electrical and Control Engineering, School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an 710021, China;
2 School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China;
3 Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N. W., Calgary, Alberta T2 N;
1 N4, Canada |
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Abstract We present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupling of the Stokes and Darcy-Forchheimer problems. Our method compiles the interface conditions of the coupled problems into the networks properly and can be served as an efficient alternative to the complex coupled problems. To impose energy conservation constraints, the CDNNs utilize simple fully connected layers and a custom loss function to perform the model training process as well as the physical property of the exact solution. The approach can be beneficial for the following reasons: Firstly, we sample randomly and only input spatial coordinates without being restricted by the nature of samples. Secondly, our method is meshfree, which makes it more efficient than the traditional methods. Finally, the method is parallel and can solve multiple variables independently at the same time. We present the theoretical results to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution. Some numerical experiments are performed and discussed to demonstrate performance of the proposed method.
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Received: 07 April 2022
Revised: 18 May 2022
Accepted manuscript online: 02 June 2022
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PACS:
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02.30.Jr
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(Partial differential equations)
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47.11.-j
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(Computational methods in fluid dynamics)
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07.05.Tp
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(Computer modeling and simulation)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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| Fund: Project supported in part by the National Natural Science Foundation of China (Grant No. 11771259), the Special Support Program to Develop Innovative Talents in the Region of Shaanxi Province, the Innovation Team on Computationally Efficient Numerical Methods Based on New Energy Problems in Shaanxi Province, and the Innovative Team Project of Shaanxi Provincial Department of Education (Grant No. 21JP013). |
Corresponding Authors:
Jian Li
E-mail: jianli@sust.edu.cn,jiaaanli@gmail.com
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Cite this article:
Jing Yue(岳靖), Jian Li(李剑), Wen Zhang(张文), and Zhangxin Chen(陈掌星) The coupled deep neural networks for coupling of the Stokes and Darcy-Forchheimer problems 2023 Chin. Phys. B 32 010201
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