KMS Of Academy of mathematics and systems sciences, CAS
Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes | |
Zhou, Zijian1,2; Wang, Li3,4,5; Yan, Zhenya1,2 | |
2022-10-31 | |
发表期刊 | PHYSICS LETTERS A |
ISSN | 0375-9601 |
卷号 | 450页码:15 |
摘要 | We introduce a deep neural network learning scheme to discover the Backlund transforms (BTs) of soliton evolution equations and an enhanced deep learning scheme for data-driven soliton equation discovery based on the known BTs, respectively. The first deep learning scheme takes advantage of some solution (or soliton equation) informations to train the data-driven BT discovery, and is valid in the study of the BT of the sine-Gordon equation, and complex and real Miura transforms between the defocusing (focusing) mKdV equation and KdV equation, as well as the data-driven mKdV equation discovery via the Miura transforms. The second deep learning scheme uses the higher-order solitons generated by the explicit/implicit BTs to study the data-driven discoveries of mKdV and sine-Gordon equations, in which the high-order soliton informations are more powerful for the enhanced leaning soliton equations with higher accuracies. (C) 2022 Elsevier B.V. All rights reserved. |
关键词 | Deep neural networks B?cklund transform Miura transform Soliton equations Breathers Solitons |
DOI | 10.1016/j.physleta.2022.128373 |
收录类别 | SCI |
语种 | 英语 |
资助项目 | National Natural Science Foun- dation of China (NSFC)[11925108] |
WOS研究方向 | Physics |
WOS类目 | Physics, Multidisciplinary |
WOS记录号 | WOS:000869433000001 |
出版者 | ELSEVIER |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/60783 |
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, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China 4.Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China 5.Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China |
推荐引用方式 GB/T 7714 | Zhou, Zijian,Wang, Li,Yan, Zhenya. Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes[J]. PHYSICS LETTERS A,2022,450:15. |
APA | Zhou, Zijian,Wang, Li,&Yan, Zhenya.(2022).Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes.PHYSICS LETTERS A,450,15. |
MLA | Zhou, Zijian,et al."Data-driven discoveries of B?cklund transformations and soliton evolution equations via deep neural network learning schemes".PHYSICS LETTERS A 450(2022):15. |
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