The coupled deep neural networks for coupling of the Stokes and Darcy–Forchheimer problems

Yue Jing; Li Jian; Zhang Wen; Chen Zhangxin

doi:10.1088/1674-1056/ac7554

Volume 32 Issue 1

May. 2023

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JOURNAL OF MECHANICAL ENGINEERING > 2023 > 32(1): 010201.

Yue Jing, Li Jian, Zhang Wen, Chen Zhangxin. The coupled deep neural networks for coupling of the Stokes and Darcy–Forchheimer problems[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 32(1): 010201. doi: 10.1088/1674-1056/ac7554

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Yue Jing, Li Jian, Zhang Wen, Chen Zhangxin. The coupled deep neural networks for coupling of the Stokes and Darcy–Forchheimer problems[J]. JOURNAL OF MECHANICAL ENGINEERING, 2023, 32(1): 010201. doi: 10.1088/1674-1056/ac7554

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The coupled deep neural networks for coupling of the Stokes and Darcy–Forchheimer problems

doi: 10.1088/1674-1056/ac7554

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 T2N 1N4,Canada

Received Date: 07 Apr 2022
Available Online: 16 May 2023
Issue Publish Date: 01 Jan 2023

Abstract

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.
- scientific computing,
- machine learning,
- the Stokes equations,
- Darcy-Forchheimer problems,
- Beavers-Joseph-Saffman interface condition

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The coupled deep neural networks for coupling of the Stokes and Darcy–Forchheimer problems

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