Dynamic mode decomposition for Koopman spectral analysis of elementary cellular automata

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

*この研究の対応する著者

研究成果: Article査読

抄録

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.

本文言語English
論文番号013125
ジャーナルChaos
34
1
DOI
出版ステータスPublished - 2024 1月 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学一般
  • 応用数学

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