A deep learning method for solving high-order nonlinear soliton equations

Shikun Cui; Zhen Wang; Jiaqi Han; Xinyu Cui; Qicheng Meng

doi:10.1088/1572-9494/ac7202

A deep learning method for solving high-order nonlinear soliton equations

Shikun Cui
, Zhen Wang^*
, Jiaqi Han
, Xinyu Cui
, Qicheng Meng

^*此作品的通讯作者

Dalian University of Technology
Ministry of Natural Resources of the People's Republic of China
Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province

科研成果: 期刊稿件 › 文章 › 同行评审

15 引用（Scopus）

摘要

We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higher-order nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg-de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.

源语言	英语
文章编号	075007
期刊	Communications in Theoretical Physics
卷	74
期	7
DOI	https://doi.org/10.1088/1572-9494/ac7202
出版状态	已出版 - 1 7月 2022
已对外发布	是

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title = "A deep learning method for solving high-order nonlinear soliton equations",

abstract = "We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higher-order nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg-de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.",

keywords = "deep learning method, high-order nonlinear soliton equations, interaction between solitons, physics-informed neural networks, the numerical driven solution",

author = "Shikun Cui and Zhen Wang and Jiaqi Han and Xinyu Cui and Qicheng Meng",

note = "Publisher Copyright: {\textcopyright} 2022 Institute of Theoretical Physics CAS, Chinese Physical Society and IOP Publishing.",

year = "2022",

month = jul,

day = "1",

doi = "10.1088/1572-9494/ac7202",

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journal = "Communications in Theoretical Physics",

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TY - JOUR

T1 - A deep learning method for solving high-order nonlinear soliton equations

AU - Cui, Shikun

AU - Wang, Zhen

AU - Han, Jiaqi

AU - Cui, Xinyu

AU - Meng, Qicheng

PY - 2022/7/1

Y1 - 2022/7/1

N2 - We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higher-order nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg-de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.

AB - We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higher-order nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg-de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.

KW - deep learning method

KW - high-order nonlinear soliton equations

KW - interaction between solitons

KW - physics-informed neural networks

KW - the numerical driven solution

UR - https://www.scopus.com/pages/publications/85134736692

U2 - 10.1088/1572-9494/ac7202

DO - 10.1088/1572-9494/ac7202

M3 - 文章

AN - SCOPUS:85134736692

SN - 0253-6102

VL - 74

JO - Communications in Theoretical Physics

JF - Communications in Theoretical Physics

IS - 7

M1 - 075007

ER -

A deep learning method for solving high-order nonlinear soliton equations

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