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MetaPINNs: Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization |
| Yanan Guo(郭亚楠)1,2,3,†, Xiaoqun Cao(曹小群)1,2,‡, Junqiang Song(宋君强)1,2, and Hongze Leng(冷洪泽)1 |
1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China;
2 College of Computer, National University of Defense Technology, Changsha 410073, China;
3 Naval Aviation University, Huludao 125001, China |
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Abstract Efficiently solving partial differential equations (PDEs) is a long-standing challenge in mathematics and physics research. In recent years, the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations. Among them, physics-informed neural networks (PINNs) are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena. In the field of nonlinear science, solitary waves and rogue waves have been important research topics. In this paper, we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints. In addition, we employ meta-learning optimization to speed up the training process. We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves. We evaluate the accuracy of the prediction results by error analysis. The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.
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Received: 25 September 2023
Revised: 06 November 2023
Accepted manuscript online: 13 November 2023
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PACS:
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02.60.Cb
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(Numerical simulation; solution of equations)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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02.30.Jr
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(Partial differential equations)
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05.45.Yv
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(Solitons)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 42005003 and 41475094). |
Corresponding Authors:
Yanan Guo, Xiaoqun Cao
E-mail: guoyn14@lzu.edu.cn;caoxiaoqun@nudt.edu.cn
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Cite this article:
Yanan Guo(郭亚楠), Xiaoqun Cao(曹小群), Junqiang Song(宋君强), and Hongze Leng(冷洪泽) MetaPINNs: Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization 2024 Chin. Phys. B 33 020203
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