Learning Koopman invariant subspaces for dynamic mode decomposition

Naoya Takeishi, Yoshinobu Kawahara, Takehisa Yairi

Research output: Contribution to journalConference article

18 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1131-1141
Number of pages11
JournalAdvances in Neural Information Processing Systems
Volume2017-December
Publication statusPublished - Jan 1 2017
Externally publishedYes
Event31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
Duration: Dec 4 2017Dec 9 2017

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Nonlinear dynamical systems
Spectrum analysis
Decomposition
Linear regression
Neural networks

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Learning Koopman invariant subspaces for dynamic mode decomposition. / Takeishi, Naoya; Kawahara, Yoshinobu; Yairi, Takehisa.

In: Advances in Neural Information Processing Systems, Vol. 2017-December, 01.01.2017, p. 1131-1141.

Research output: Contribution to journalConference article

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