Learning Koopman invariant subspaces for dynamic mode decomposition

Naoya Takeishi, Yoshinobu Kawahara, Takehisa Yairi

研究成果: Contribution to journalConference article査読

84 被引用数 (Scopus)

抄録

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynamics, which is not always possible since we may not have any a priori knowledge about them. In this paper, we propose a fully data-driven method for Koopman spectral analysis based on the principle of learning Koopman invariant subspaces from observed data. To this end, we propose minimization of the residual sum of squares of linear least-squares regression to estimate a set of functions that transforms data into a form in which the linear regression fits well. We introduce an implementation with neural networks and evaluate performance empirically using nonlinear dynamical systems and applications.

本文言語英語
ページ(範囲)1131-1141
ページ数11
ジャーナルAdvances in Neural Information Processing Systems
2017-December
出版ステータス出版済み - 2017
外部発表はい
イベント31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, 米国
継続期間: 12 4 201712 9 2017

All Science Journal Classification (ASJC) codes

  • コンピュータ ネットワークおよび通信
  • 情報システム
  • 信号処理

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