Krylov subspace method for nonlinear dynamical systems with random noise

Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda, Yoichi Matsuo, Yoshinobu Kawahara

研究成果: Contribution to journalArticle査読

2 被引用数 (Scopus)

抄録

Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this paper, we address a lifted representation of nonlinear dynamical systems with random noise based on transfer operators, and develop a novel Krylov subspace method for estimating the operators using finite data, with consideration of the unboundedness of operators. For this purpose, we first consider Perron-Frobenius operators with kernel-mean embeddings for such systems. We then extend the Arnoldi method, which is the most classical type of Kryov subspace methods, so that it can be applied to the current case. Meanwhile, the Arnoldi method requires the assumption that the operator is bounded, which is not necessarily satisfied for transfer operators on nonlinear systems. We accordingly develop the shift-invert Arnoldi method for Perron-Frobenius operators to avoid this problem. Also, we describe an approach of evaluating predictive accuracy by estimated operators on the basis of the maximum mean discrepancy, which is applicable, for example, to anomaly detection in complex systems. The empirical performance of our methods is investigated using synthetic and real-world healthcare data.

本文言語英語
ジャーナルJournal of Machine Learning Research
21
出版ステータス出版済み - 8 2020

All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 制御およびシステム工学
  • 統計学および確率
  • 人工知能

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