CSpace
Data-Driven Deep Learning for The Multi-Hump Solitons and Parameters Discovery in NLS Equations with Generalized PT-Scarf-II Potentials
Zhong, Ming1,2; Zhang, Jian-Guo3; Zhou, Zijian1,2; Tian, Shou-Fu3; Yan, Zhenya1,2
2022-07-28
Source PublicationNEURAL PROCESSING LETTERS
ISSN1370-4621
Pages19
AbstractIn 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.
KeywordFocusing and defocusing nonlinear Schrodinger equations Generalized PT-Scarf-II potential Physics-informed deep neural networks Data-driven solitons and parameters discovery
DOI10.1007/s11063-022-10979-3
Indexed BySCI
Language英语
Funding ProjectNSFC[11975306] ; NSFC[11925108] ; NSFC[11731014] ; NSF of Jiangsu Province of China[BK20181351] ; Six Talent Peaks Project in Jiangsu Province[JY-059]
WOS Research AreaComputer Science
WOS SubjectComputer Science, Artificial Intelligence
WOS IDWOS:000832532300001
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61131
Collection中国科学院数学与系统科学研究院
Corresponding AuthorYan, Zhenya
Affiliation1.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
Recommended Citation
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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Zhong, Ming]'s Articles
[Zhang, Jian-Guo]'s Articles
[Zhou, Zijian]'s Articles
Baidu academic
Similar articles in Baidu academic
[Zhong, Ming]'s Articles
[Zhang, Jian-Guo]'s Articles
[Zhou, Zijian]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Zhong, Ming]'s Articles
[Zhang, Jian-Guo]'s Articles
[Zhou, Zijian]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.