Number of Solitons Emerged in the Initial Profile of Shallow Water Using Convolutional Neural Networks

作     者：WANG Zhen CUI Shikun WANG Zhen;CUI Shikun

作者机构：School of Mathematical SciencesDalian University of TechnologyDalian 116024China School of Mathematical SciencesBeihang UniversityBeijing 100191China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2024年第37卷第2期

页      面：463-479页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 070102[理学-计算数学] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Science Foundation of China under Grant Nos.52171251,U2106225,52231011 Dalian Science and Technology Innovation Fund under Grant No.2022JJ12GX036 

主　　题：Convolutional neural network deep learning method KdV equation soliton 

摘      要：The soliton resolution conjecture proposes that the initial value problem can evolve into a dispersion part and a soliton ***,the problem of determining the number of solitons that form in a given initial profile remains unsolved,except for a few specific *** this paper,the authors use the deep learning method to predict the number of solitons in a given initial value of the Korteweg-de Vries(KdV)*** leveraging the analytical relationship between Asech^(2)(x)initial values and the number of solitons,the authors train a Convolutional Neural Network(CNN)that can accurately identify the soliton count from spatio-temporal *** trained neural network is capable of predicting the number of solitons with other given initial values without any additional *** extensive calculations,the authors demonstrate the effectiveness and high performance of the proposed method.