Data-Driven Deep Learning for The Multi-Hump Solitons and Parameters Discovery in NLS Equations with Generalized PT-Scarf-II Potentials

doi:10.1007/s11063-022-10979-3

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	Data-Driven Deep Learning for The Multi-Hump Solitons and Parameters Discovery in NLS Equations with Generalized PT-Scarf-II Potentials
	Zhong, Ming 1,2; Zhang, Jian-Guo 3; Zhou, Zijian 1,2; Tian, Shou-Fu 3; Yan, Zhenya 1,2
	2022-07-28
发表期刊	NEURAL PROCESSING LETTERS
ISSN	1370-4621
页码	19
摘要	In this paper, we investigate the data-driven forward and inverse problems of both the focusing and defocusing nonlinear Schrodinger equations (NLSEs) with generalized parity-time (PT)-Scarf-II potential via the physics-informed neural networks (PINNs) deep learning. The NLSE with four different initial conditions and periodic boundary condition are analyzed via the PINNs approach. And the predicted (data-driven) multi-hump solitons have been compared to the solutions, which can be obtained from the analytical or the high-accuracy numerical methods. Moreover, we explore the influences of several key factors (e.g., the depth of the neural networks, activation functions) on the performance of the PINNs algorithm. Finally, the data-driven inverse problems of the NLSE are also investigated such that the coefficients of the generalized PT-Scarf-II potentials, the nonlinear and dispersion terms can be found. The results obtained in this paper can be used to further explore the NLSE with PT-symmetric potentials and the applications of deep learning method in the nonlinear partial differential equations.
关键词	Focusing and defocusing nonlinear Schrodinger equations Generalized PT-Scarf-II potential Physics-informed deep neural networks Data-driven solitons and parameters discovery
DOI	10.1007/s11063-022-10979-3
收录类别	SCI
语种	英语
资助项目	NSFC[11975306] ; NSFC[11925108] ; NSFC[11731014] ; NSF of Jiangsu Province of China[BK20181351] ; Six Talent Peaks Project in Jiangsu Province[JY-059]
WOS研究方向	Computer Science
WOS类目	Computer Science, Artificial Intelligence
WOS记录号	WOS:000832532300001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61131
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Zhenya
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China
推荐引用方式 GB/T 7714	Zhong, Ming,Zhang, Jian-Guo,Zhou, Zijian,et al. Data-Driven Deep Learning for The Multi-Hump Solitons and Parameters Discovery in NLS Equations with Generalized PT-Scarf-II Potentials[J]. NEURAL PROCESSING LETTERS,2022:19.
APA	Zhong, Ming,Zhang, Jian-Guo,Zhou, Zijian,Tian, Shou-Fu,&Yan, Zhenya.(2022).Data-Driven Deep Learning for The Multi-Hump Solitons and Parameters Discovery in NLS Equations with Generalized PT-Scarf-II Potentials.NEURAL PROCESSING LETTERS,19.
MLA	Zhong, Ming,et al."Data-Driven Deep Learning for The Multi-Hump Solitons and Parameters Discovery in NLS Equations with Generalized PT-Scarf-II Potentials".NEURAL PROCESSING LETTERS (2022):19.