Learning Topological Horseshoe via Deep Neural Networks

被引：1

作者：

Yang, Xiao-Song ^{[1
,2
]}

Cheng, Junfeng ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2024年 / 34卷 / 04期

关键词：

Poincare map; topological horseshoe; chaos; deep neural network;

D O I：

10.1142/S021812742430009X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Deep Neural Networks (DNNs) have been successfully applied to investigations of numerical dynamics of finite-dimensional nonlinear systems such as ODEs instead of finding numerical solutions to ODEs via the traditional Runge-Kutta method and its variants. To show the advantages of DNNs, in this paper, we demonstrate that the DNNs are more efficient in finding topological horseshoes in chaotic dynamical systems.

引用

页数：11

共 50 条

[31] Artificial neural networks and deep learning
Geubbelmans, Melvin
Rousseau, Axel-Jan
Burzykowski, Tomasz
Valkenborg, Dirk
AMERICAN JOURNAL OF ORTHODONTICS AND DENTOFACIAL ORTHOPEDICS, 2024, 165 (02) : 248 - 251
[32] Shortcut learning in deep neural networks
Robert Geirhos
Jörn-Henrik Jacobsen
Claudio Michaelis
Richard Zemel
Wieland Brendel
Matthias Bethge
Felix A. Wichmann
Nature Machine Intelligence, 2020, 2 : 665 - 673
[33] Fast learning in Deep Neural Networks
Chandra, B.
Sharma, Rajesh K.
NEUROCOMPUTING, 2016, 171 : 1205 - 1215
[34] A topological deep learning framework for neural spike decoding
Mitchell, Edward C.
Story, Brittany
Boothe, David
Franaszczuk, Piotr J.
Maroulas, Vasileios
BIOPHYSICAL JOURNAL, 2024, 123 (17) : 2781 - 2789
[35] Deep associative learning for neural networks
Liu, Jia
Zhang, Wenhua
Liu, Fang
Xiao, Liang
NEUROCOMPUTING, 2021, 443 (443) : 222 - 234
[36] Collaborative Learning for Deep Neural Networks
Song, Guocong
Chai, Wei
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 31 (NIPS 2018), 2018, 31
[37] Big learning and deep neural networks
Montavon, Grégoire
Müller, Klaus-Robert
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012, 7700 LECTURE NO : 419 - 420
[38] Multiplierless Neural Networks for Deep Learning
Banduka, Maja Lutovac
Lutovac, Miroslav
2024 13TH MEDITERRANEAN CONFERENCE ON EMBEDDED COMPUTING, MECO 2024, 2024, : 262 - 265
[39] Shortcut learning in deep neural networks
Geirhos, Robert
Jacobsen, Joern-Henrik
Michaelis, Claudio
Zemel, Richard
Brendel, Wieland
Bethge, Matthias
Wichmann, Felix A.
NATURE MACHINE INTELLIGENCE, 2020, 2 (11) : 665 - 673
[40] Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks
Zhang, Wenrui
Li, Peng
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 33, NEURIPS 2020, 2020, 33

← 1 2 3 4 5 →