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

	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
刊名	NEURAL PROCESSING LETTERS
	2022-07-28
页码	19
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
ISSN号	1370-4621
DOI	10.1007/s11063-022-10979-3
英文摘要	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.
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
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000832532300001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61130]
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.