Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata-Reference-Cited by-同舟云学术

Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata

Published:2024-01-01 Issue:1 Volume:34 Page:
ISSN:1054-1500
Container-title:Chaos: An Interdisciplinary Journal of Nonlinear Science
language:en
Short-container-title:

Author:

Taga Keisuke¹^ORCID,Kato Yuzuru²^ORCID,Yamazaki Yoshihiro¹^ORCID,Kawahara Yoshinobu³⁴^ORCID,Nakao Hiroya⁵^ORCID

Affiliation:

1. Department of Physics, School of Advanced Science and Engineering, Waseda University 1 , Tokyo 169-8555, Japan

2. Department of Complex and Intelligent Systems, School of Systems Information Science, Future University Hakodate 2 , Hakodate, Hokkaido 041-8655, Japan

3. Graduate School of Information Science and Technology, Osaka University 3 , Osaka 565-0871, Japan and , Tokyo 103-0027, Japan

4. Center for Advanced Intelligence Project, RIKEN 3 , Osaka 565-0871, Japan and , Tokyo 103-0027, Japan

5. Department of Systems and Control Engineering, School of Engineering, Tokyo Institute of Technology 4 , Tokyo 152-8552, Japan

Abstract

We apply dynamic mode decomposition (DMD) to elementary cellular automata (ECA). Three types of DMD methods are considered, and the reproducibility of the system dynamics and Koopman eigenvalues from observed time series is investigated. While standard DMD fails to reproduce the system dynamics and Koopman eigenvalues associated with a given periodic orbit in some cases, Hankel DMD with delay-embedded time series improves reproducibility. However, Hankel DMD can still fail to reproduce all the Koopman eigenvalues in specific cases. We propose an extended DMD method for ECA that uses nonlinearly transformed time series with discretized Walsh functions and show that it can completely reproduce the dynamics and Koopman eigenvalues. Linear-algebraic backgrounds for the reproducibility of the system dynamics and Koopman eigenvalues are also discussed.

Funder

Japan Society for the Promotion of Science

Core Research for Evolutional Science and Technology

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0159069/18701937/013125_1_5.0159069.pdf

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