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Development of data-driven reduced-order modeling framework for large dimensional dynamical systems and applications to vital sign signals

Research Project

Project/Area Number 17H03279
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering/System engineering
Research InstitutionTokyo Institute of Technology

Principal Investigator

Nakao Hiroya  東京工業大学, 工学院, 教授 (40344048)

Co-Investigator(Kenkyū-buntansha) 小林 亮太  東京大学, 大学院新領域創成科学研究科, 准教授 (70549237)
秦 重史  鹿児島大学, 理工学域理学系, 准教授 (70735927)
紅林 亘  弘前大学, 教育推進機構, 助教 (70761211)
河村 洋史  国立研究開発法人海洋研究開発機構, 付加価値情報創生部門(数理科学・先端技術研究開発センター), グループリーダー (90455494)
Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥17,680,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥4,080,000)
Fiscal Year 2020: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2019: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2018: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2017: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Keywords非線形ダイナミクス / 力学系 / 縮約理論 / 非線形振動子 / 同期現象 / Koopman作用素 / 生体リズム / 動的モード分解 / 非線形振動 / 縮約 / 非線形力学系 / 次元縮約 / データ同化 / バイタルサイン / 複雑系
Outline of Final Research Achievements

Reduced-order modeling methods for nonlinear dynamical systems with large degrees of freedom have been developed. Theoretical frameworks for deriving reduced mathematical models for small sets of key variables representing the essential dynamics have been established for various types of nonlinear dynamical systems. Data-driven modeling methods for the phenomena whose mathematical models are unknown have also been considered. Dynamical reduction theories, in particular, the classical phase reduction theory for nonlinear oscillations, have been extended to phase-amplitude reduction theory for high-dimensional dynamical systems with many dynamical modes and also to infinite-dimensional systems described by partial differential equations. The study has been performed from the modern viewpoint of Koopman operator theory and also newly extended to fluid mechanical systems and to quantum dissipative systems.

Academic Significance and Societal Importance of the Research Achievements

実世界の様々な系は多様な非線形ダイナミクスを示し、それは時に重要な機能的役割を果たす。その典型例として、例えば生体における心臓の拍動や呼吸などのリズムが挙げられる。そのような系は、しばしば非常に高次元の数理モデルで記述されるため、その解析には、系の本質的な自由度に着目して次元縮約された低次元モデルを導くことが重要である。本研究では、様々な非線形力学系に対して、近年発展の著しい作用素論的な観点からの縮約モデリング手法を開発した。この手法は、実世界の様々な系の運動の解析や制御に役立つことが期待される。

Report

(5 results)
  • 2022 Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (52 results)

All 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (3 results) Journal Article (30 results) (of which Int'l Joint Research: 10 results,  Peer Reviewed: 30 results,  Open Access: 17 results) Presentation (16 results) (of which Int'l Joint Research: 14 results,  Invited: 6 results) Book (1 results) Remarks (1 results) Funded Workshop (1 results)

  • [Int'l Joint Research] University of Namur(ベルギー)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Czech Academy of Sciences(チェコ)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Namur大学(ベルギー)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Phase-reduction for synchronization of oscillating flow by perturbation on surrounding structure2021

    • Author(s)
      Loe, I. A., Nakao H, Jimbo Y., and Kotani K.
    • Journal Title

      Journal of Fluid Mechanics

      Volume: 911 Pages: 1-12

    • DOI

      10.1017/jfm.2020.1110

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Instantaneous phase synchronization of two decoupled quantum limit-cycle oscillators induced by conditional photon detection2021

    • Author(s)
      Kato Yuzuru、Nakao Hiroya
    • Journal Title

      Physical Review Research

      Volume: 3 Issue: 1 Pages: 013085-013085

    • DOI

      10.1103/physrevresearch.3.013085

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quantum coherence resonance2021

    • Author(s)
      Kato Yuzuru、Nakao Hiroya
    • Journal Title

      New Journal of Physics

      Volume: 23 Issue: 4 Pages: 043018-043018

    • DOI

      10.1088/1367-2630/abf1d7

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Stable plane waves in nonlocally coupled phase oscillators2021

    • Author(s)
      Yoji Kawamura
    • Journal Title

      AIP Advances

      Volume: 11 Issue: 1 Pages: 1-16

    • DOI

      10.1063/5.0035637

    • NAID

      130008156627

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Sparse optimization of mutual synchronization in collectively oscillating networks2021

    • Author(s)
      Nakao Hiroya、Yamaguchi Katsunori、Katayama Shingo、Yanagita Tatsuo
    • Journal Title

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      Volume: 31 Issue: 6 Pages: 063113-063113

    • DOI

      10.1063/5.0049091

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Koopman spectral analysis of elementary cellular automata2021

    • Author(s)
      Keisuke Taga, Yuzuru Kato, Yoshinobu Kawahara, Yoshihiro Yamazaki, and Hiroya Nakao
    • Journal Title

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      Volume: 31 Issue: 10 Pages: 103121-103121

    • DOI

      10.1063/5.0059202

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory2021

    • Author(s)
      Takata Shohei、Kato Yuzuru、Nakao Hiroya
    • Journal Title

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      Volume: 31 Issue: 9 Pages: 093124-093124

    • DOI

      10.1063/5.0054603

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators2021

    • Author(s)
      Kato Yuzuru、Zlotnik Anatoly、Li Jr-Shin、Nakao Hiroya
    • Journal Title

      Nonlinear Dynamics

      Volume: 105 Issue: 3 Pages: 2247-2263

    • DOI

      10.1007/s11071-021-06703-w

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory2021

    • Author(s)
      Kato Yuzuru、Zhu Jinjie、Kurebayashi Wataru、Nakao Hiroya
    • Journal Title

      Mathematics

      Volume: 9 Issue: 18 Pages: 2188-2188

    • DOI

      10.3390/math9182188

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Enhancement of quantum synchronization via continuous measurement and feedback control2021

    • Author(s)
      Kato Yuzuru、Nakao Hiroya
    • Journal Title

      New Journal of Physics

      Volume: 23 Issue: 1 Pages: 013007-013007

    • DOI

      10.1088/1367-2630/abd7be

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Stochastic periodic orbits in fast-slow systems with self-induced stochastic resonance2021

    • Author(s)
      Zhu Jinjie、Nakao Hiroya
    • Journal Title

      Physical Review Research

      Volume: 3 Issue: 3 Pages: 1-11

    • DOI

      10.1103/physrevresearch.3.033070

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Spectral analysis of the Koopman operator for partial differential equations2020

    • Author(s)
      Nakao Hiroya、Mezic Igor
    • Journal Title

      Chaos: An Interdisciplinary Journal of Nonlinear Science

      Volume: 30 Issue: 11 Pages: 113131-113131

    • DOI

      10.1063/5.0011470

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Nonlinear phase-amplitude reduction of delay-induced oscillations2020

    • Author(s)
      Kotani Kiyoshi、Ogawa Yutaro、Shirasaka Sho、Akao Akihiko、Jimbo Yasuhiko、Nakao Hiroya
    • Journal Title

      Physical Review Research

      Volume: 2 Issue: 3 Pages: 033106-033122

    • DOI

      10.1103/physrevresearch.2.033106

    • NAID

      120006953169

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Phase-Amplitude Reduction of Limit Cycling Systems2020

    • Author(s)
      Shirasaka Sho、Kurebayashi Wataru、Nakao Hiroya
    • Journal Title

      The Koopman Operator in Systems and Control, Lecture Notes in Control and Information Sciences 484, Springer Nature

      Volume: 484 Pages: 383-417

    • DOI

      10.1007/978-3-030-35713-9_15

    • ISBN
      9783030357122, 9783030357139
    • Related Report
      2020 Annual Research Report 2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Turing patterns in a network-reduced FitzHugh-Nagumo model2020

    • Author(s)
      Carletti Timoteo、Nakao Hiroya
    • Journal Title

      Physical Review E

      Volume: 101 Issue: 2 Pages: 022203-0222015

    • DOI

      10.1103/physreve.101.022203

    • NAID

      120006953174

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators2020

    • Author(s)
      Kato Yuzuru、Nakao Hiroya
    • Journal Title

      Physical Review E

      Volume: 101 Issue: 1 Pages: 012210-012219

    • DOI

      10.1103/physreve.101.012210

    • NAID

      120006953175

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Chaotic Encryption for Belief Propagation Decoding in Massive MIMO Systems2020

    • Author(s)
      Sakoda K.、Hata H.、Hata S.
    • Journal Title

      Journal of Communications Technology and Electronics

      Volume: 65 Issue: 2 Pages: 172-178

    • DOI

      10.1134/s1064226920020175

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the concept of dynamical reduction: the case of coupled oscillators2019

    • Author(s)
      Kuramoto Yoshiki、Nakao Hiroya
    • Journal Title

      Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

      Volume: 377 Issue: 2160 Pages: 20190041-20190041

    • DOI

      10.1098/rsta.2019.0041

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semiclassical phase reduction theory for quantum synchronization2019

    • Author(s)
      Kato Yuzuru、Yamamoto Naoki、Nakao Hiroya
    • Journal Title

      Physical Review Research

      Volume: 1 Issue: 3 Pages: 033012-0330127

    • DOI

      10.1103/physrevresearch.1.033012

    • NAID

      120006953178

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators2019

    • Author(s)
      Watanabe Nobuhiro、Kato Yuzuru、Shirasaka Sho、Nakao Hiroya
    • Journal Title

      Physical Review E

      Volume: 100 Issue: 4 Pages: 042205-0422020

    • DOI

      10.1103/physreve.100.042205

    • NAID

      120006953177

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Suppression of Macroscopic Oscillations in Mixed Populations of Active and Inactive Oscillators Coupled through Lattice Laplacian2019

    • Author(s)
      Ikuhiro Yamaguchi, Takuya Isomura, Hiroya Nakao, Yutaro Ogawa, Yasuhiko Jimbo, Kiyoshi Kotani
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 88 Issue: 5 Pages: 054004-054004

    • DOI

      10.7566/jpsj.88.054004

    • NAID

      40021885761

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Phase reduction of limit-torus solutions to partial differential algebraic equations2019

    • Author(s)
      Yoji Kawamura
    • Journal Title

      Physical Review Research

      Volume: 1 Issue: 3 Pages: 1-23

    • DOI

      10.1103/physrevresearch.1.033130

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Critical size of neural population for reliable information transmission2019

    • Author(s)
      Kostal Lubomir、Kobayashi Ryota
    • Journal Title

      Physical Review E

      Volume: 100 Issue: 5

    • DOI

      10.1103/physreve.100.050401

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Modeling cochlear two-tone suppression using a system of nonlinear oscillators with feed-forward coupling2019

    • Author(s)
      Ouchi Masanori、Nakao Hiroya
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 10 Issue: 1 Pages: 90-99

    • DOI

      10.1587/nolta.10.90

    • NAID

      130007542462

    • ISSN
      2185-4106
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations2018

    • Author(s)
      Hiroya Nakao, Sho Yasui, Masashi Ota, Kensuke Arai, and Yoji Kawamura
    • Journal Title

      Chaos

      Volume: 28 Issue: 4 Pages: 045103-045103

    • DOI

      10.1063/1.5009669

    • NAID

      120006953245

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Phase-response analysis of synchronization for periodic flows2018

    • Author(s)
      Taira Kunihiko、Nakao Hiroya
    • Journal Title

      Journal of Fluid Mechanics

      Volume: 846

    • DOI

      10.1017/jfm.2018.327

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Phase reduction approach to elastohydrodynamic synchronization of beating flagella2018

    • Author(s)
      Yoji Kawamura and Remi Tsubaki
    • Journal Title

      Physical Review E

      Volume: 97 Issue: 2 Pages: 1-1

    • DOI

      10.1103/physreve.97.022212

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling2017

    • Author(s)
      Shirasaka Sho、Watanabe Nobuhiro、Kawamura Yoji、Nakao Hiroya
    • Journal Title

      Physical Review E

      Volume: 96 Issue: 1

    • DOI

      10.1103/physreve.96.012223

    • NAID

      120006582613

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems2017

    • Author(s)
      Kawamura Yoji、Shirasaka Sho、Yanagita Tatsuo、Nakao Hiroya
    • Journal Title

      Physical Review E

      Volume: 96 Issue: 1 Pages: 012224-012236

    • DOI

      10.1103/physreve.96.012224

    • NAID

      120006582616

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Localization of Laplacian eigenvectors on random networks2017

    • Author(s)
      Shigefumi Hata and Hiroya Nakao
    • Journal Title

      Scientific Reports

      Volume: 7 Issue: 1 Pages: 1121-1121

    • DOI

      10.1038/s41598-017-01010-0

    • NAID

      120006582596

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Continuous Measurement and Feedback Control for Enhancement of Quantum Synchronization2020

    • Author(s)
      Yuzuru Kato and Hiroya Nakao
    • Organizer
      Proceedings of the 59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea (Virtual)
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Reduced Dynamical Description of Collective Oscillations in Populations of Coupled Dynamical Elements2020

    • Author(s)
      Hiroya Nakao
    • Organizer
      IFAC 2020 Berlin pre-conference workshop “Analysis, Control, and Learning of Dynamic Ensemble and Population Systems" (online)
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Optimal Waveform for Fast Entrainment of Weakly Forced Quantum Nonlinear Dissipative Oscillators2019

    • Author(s)
      Yuzuru Kato and Hiroya Nakao
    • Organizer
      58th IEEE Conference on Decision and Control, Nice, France, December 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Collective oscillations and synchronization in networks of coupled dynamical elements2019

    • Author(s)
      Hiroya Nakao
    • Organizer
      Workshop on dynamical processes on networks, University of Namur, Namur, Belgium, September 5, 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Phase-amplitude reduction of rhythmic patterns in reaction-diffusion systems2019

    • Author(s)
      Hiroya Nakao
    • Organizer
      Conference on Applications of Dynamical Systems (SIAMDS19), Snowbird Ski and Summer Resort, Snowbird, Utah, USA, May 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 時間連続測定を用いた量子同期現象における振動子の位相コヒーレンスの向上2019

    • Author(s)
      加藤 譲, 中尾裕也
    • Organizer
      日本物理学会第75回年次大会 岐阜大学
    • Related Report
      2019 Annual Research Report
  • [Presentation] 半古典位相縮約理論による量子同期現象の解析2019

    • Author(s)
      加藤 譲, 中尾裕也
    • Organizer
      日本応用数理学会 2019年度 年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Koopman eigenfunctionals and reduced description of partial differential equations2019

    • Author(s)
      H. Nakao
    • Organizer
      IPAM workshop on Operator Theoretic Methods in Dynamic Data Analysis and Control, Institute for pure and applied mathematics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Phase-Amplitude Reduction, Synchronization and Control of Collective Oscillations in Networks of Dynamical Systems2018

    • Author(s)
      Hiroya Nakao
    • Organizer
      2018 Gordon Research Conference on Oscillations and Dynamic Instabilities in Chemical Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Koopman eigenfunctionals and phase-amplitude reduction of rhythmic reaction-diffusion systems2018

    • Author(s)
      Hiroya Nakao and I. Mezic
    • Organizer
      SICE Annual Conference 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Phase and amplitude description of complex oscillatory systems2018

    • Author(s)
      H. Nakao
    • Organizer
      Physics of Biological Oscillators: New Insights into Non- Equilibrium and Non-Autonomous Systems
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Phase Reduction and Synchronization of Rhythmic Spatiotemporal Patterns2018

    • Author(s)
      Hiroya Nakao
    • Organizer
      Conference and Tutorial on Analysis and Modelling of Complex Oscillatory Systems
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Turing Patterns in Reaction-diffusion Systems on Random Networks2017

    • Author(s)
      Shigefumi Hata and Hiroya Nakao
    • Organizer
      SIAM Conference on Applications of Dynamical Systems (SIAMDS17)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Optimal Parameter Selection for Extended Dynamic Mode Decomposition2017

    • Author(s)
      Wataru Kurebayashi, Sho Shirasaka and Hiroya Nakao
    • Organizer
      SIAM Conference on Applications of Dynamical Systems (SIAMDS17)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Isostable Reduction for Stable Limit-Cycling Systems2017

    • Author(s)
      Sho Shirasaka, Wataru Kurebayashi and Hiroya Nakao
    • Organizer
      SIAM Conference on Applications of Dynamical Systems (SIAMDS17)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Optimal Model Selection for Estimating Stochastic Koopman Modes2017

    • Author(s)
      Wataru Kurebayashi, Sho Shirasaka and Hiroya Nakao
    • Organizer
      2017 International Symposium on Nonlinear Theory and its Applications (NOLTA2017)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Book] (情報ネットワーク科学シリーズ 4) ネットワーク・カオス - 非線形ダイナミクス,複雑系と情報ネットワーク -2018

    • Author(s)
      中尾裕也, 長谷川幹雄, 合原一幸
    • Total Pages
      262
    • Publisher
      コロナ社
    • ISBN
      9784339028041
    • Related Report
      2017 Annual Research Report
  • [Remarks] Hiroya Nakao Papers

    • URL

      http://www.k.mei.titech.ac.jp/members/nakao/papers.html

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
  • [Funded Workshop] Workshop on dynamical processes on networks2018

    • Related Report
      2018 Annual Research Report

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Published: 2017-04-28   Modified: 2024-01-30  

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