Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata

Keisuke Taga*, Yuzuru Kato, Yoshihiro Yamazaki, Yoshinobu Kawahara, Hiroya Nakao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number013125
JournalChaos
Volume34
Issue number1
DOIs
Publication statusPublished - 2024 Jan 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics

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