### 抄録

Understanding nonlinear dynamical systems (NLDSs)is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.

元の言語 | 英語 |
---|---|

ページ（範囲） | 94-103 |

ページ数 | 10 |

ジャーナル | Neural Networks |

巻 | 117 |

DOI | |

出版物ステータス | 出版済み - 9 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Cognitive Neuroscience
- Artificial Intelligence

### これを引用

**Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables.** / Fujii, Keisuke; Kawahara, Yoshinobu.

研究成果: ジャーナルへの寄稿 › 記事

}

TY - JOUR

T1 - Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

AU - Fujii, Keisuke

AU - Kawahara, Yoshinobu

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Understanding nonlinear dynamical systems (NLDSs)is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.

AB - Understanding nonlinear dynamical systems (NLDSs)is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.

UR - http://www.scopus.com/inward/record.url?scp=85066076433&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066076433&partnerID=8YFLogxK

U2 - 10.1016/j.neunet.2019.04.020

DO - 10.1016/j.neunet.2019.04.020

M3 - Article

AN - SCOPUS:85066076433

VL - 117

SP - 94

EP - 103

JO - Neural Networks

JF - Neural Networks

SN - 0893-6080

ER -