Deciphering complexity: machine learning insights into the chaos

IF 1.6 4区 物理与天体物理 Q3 PHYSICS, CONDENSED MATTER
Lazare Osmanov
{"title":"Deciphering complexity: machine learning insights into the chaos","authors":"Lazare Osmanov","doi":"10.1140/epjb/s10051-024-00840-y","DOIUrl":null,"url":null,"abstract":"<p>We introduce new machine learning techniques for analyzing chaotic dynamical systems. The main goal of this study is to develop a simple method for calculating the Lyapunov exponent using only two trajectory data points, in contrast to traditional methods that require averaging procedures. Additionally, we explore phase transition graphs to analyze the shift from regular periodic to chaotic dynamics, focusing on identifying “almost integrable” trajectories where conserved quantities deviate from whole numbers. Furthermore, we identify “integrable regions” within chaotic trajectories. These methods are tested on two dynamical systems: “two objects moving on a rod” and the “Henon–Heiles” system.</p>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"98 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal B","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjb/s10051-024-00840-y","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
引用次数: 0

Abstract

We introduce new machine learning techniques for analyzing chaotic dynamical systems. The main goal of this study is to develop a simple method for calculating the Lyapunov exponent using only two trajectory data points, in contrast to traditional methods that require averaging procedures. Additionally, we explore phase transition graphs to analyze the shift from regular periodic to chaotic dynamics, focusing on identifying “almost integrable” trajectories where conserved quantities deviate from whole numbers. Furthermore, we identify “integrable regions” within chaotic trajectories. These methods are tested on two dynamical systems: “two objects moving on a rod” and the “Henon–Heiles” system.

解读复杂性:机器学习洞察混沌
我们介绍了新的机器学习技术来分析混沌动力系统。本研究的主要目标是开发一种简单的方法来计算李雅普诺夫指数,仅使用两个轨迹数据点,而不是传统的方法,需要平均程序。此外,我们探索相变图来分析从规则周期到混沌动力学的转变,重点是识别“几乎可积”的轨迹,其中守恒量偏离整数。此外,我们确定了混沌轨迹内的“可积区域”。这些方法在两个动力系统上进行了测试:“两个物体在一根杆上移动”和“Henon-Heiles”系统。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
The European Physical Journal B
The European Physical Journal B 物理-物理:凝聚态物理
CiteScore
2.80
自引率
6.20%
发文量
184
审稿时长
5.1 months
期刊介绍: Solid State and Materials; Mesoscopic and Nanoscale Systems; Computational Methods; Statistical and Nonlinear Physics
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信