MetaPINNs: Predicting soliton and rogue wave of nonlinear PDEs via the improved physics-informed neural networks based on meta-learned optimization

被引:0
|
作者
Guo, Yanan [1 ,2 ,3 ]
Cao, Xiaoqun [1 ,2 ]
Song, Junqiang [1 ,2 ]
Leng, Hongze [1 ]
机构
[1] Natl Univ Def Technol, Coll Meteorol & Oceanog, Changsha 410073, Peoples R China
[2] Natl Univ Def Technol, Coll Comp, Changsha 410073, Peoples R China
[3] Naval Aviat Univ, Yantai 264001, Peoples R China
基金
中国国家自然科学基金;
关键词
physics-informed neural networks; gradient-enhanced loss function; meta-learned optimization; nonlinear science; 02.60.Cb; 07.05.Mh; 02.30.Jr; 05.45.Yv;
D O I
10.1088/1674-1056/ad0bf4
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页数:12
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