메뉴 건너뛰기




Volumn 2, Issue 2, 2015, Pages 247-265

A kernel-based method for data-driven Koopman spectral analysis

Author keywords

Dynamic mode decomposition; Kernel methods; Koopman operator; Machine learning; Time series analysis

Indexed keywords


EID: 85018029552     PISSN: None     EISSN: 21582505     Source Type: Journal    
DOI: 10.3934/jcd.2015005     Document Type: Article
Times cited : (355)

References (36)
  • 1
    • 84883199345 scopus 로고    scopus 로고
    • Koopman-mode decomposition of the cylinder wake
    • S. Bagheri, Koopman-mode decomposition of the cylinder wake, Journal of Fluid Mechanics, 726 (2013), 596-623
    • (2013) Journal of Fluid Mechanics , vol.726 , pp. 596-623
    • Bagheri, S.1
  • 7
    • 27144489164 scopus 로고    scopus 로고
    • A tutorial on support vector machines for pattern recognition
    • C. J. Burges, A tutorial on support vector machines for pattern recognition, Data Mining and Knowledge Discovery, 2 (1998), 121-167
    • (1998) Data Mining and Knowledge Discovery , vol.2 , pp. 121-167
    • Burges, C.J.1
  • 8
    • 0011075775 scopus 로고    scopus 로고
    • An introduction to the proper orthogonal decomposition
    • A. Chatterjee, An introduction to the proper orthogonal decomposition, Current Science, 78 (2000), 808-817
    • (2000) Current Science , vol.78 , pp. 808-817
    • Chatterjee, A.1
  • 13
    • 0035509964 scopus 로고    scopus 로고
    • Liouvillian dynamics of the Hopf bifurcation
    • P. Gaspard and S. Tasaki, Liouvillian dynamics of the Hopf bifurcation, Physical Review E, 64 (2001), 056232, 17pp
    • (2001) Physical Review E , vol.64 , pp. 17
    • Gaspard, P.1    Tasaki, S.2
  • 14
    • 84909968774 scopus 로고    scopus 로고
    • Dynamic mode decomposition for large and streaming datasets
    • M. S. Hemati, M. O. Williams and C. W. Rowley, Dynamic mode decomposition for large and streaming datasets, Physics of Fluids, 26 (2014), 111701
    • (2014) Physics of Fluids , vol.26
    • Hemati, M.S.1    Williams, M.O.2    Rowley, C.W.3
  • 15
    • 85009173821 scopus 로고    scopus 로고
    • Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, 2nd edition
    • P. Holmes, J. L. Lumley, G. Berkooz and C. W. Rowley, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, 2nd edition, 2012
    • (2012) Turbulence
    • Holmes, P.1    Lumley, J.L.2    Berkooz, G.3    Rowley, C.W.4
  • 23
    • 21844455782 scopus 로고    scopus 로고
    • Spectral properties of dynamical systems. model reduction and decompositions
    • I. Mezić, Spectral properties of dynamical systems, model reduction and decompositions, Nonlinear Dynamics, 41 (2005), 309-325
    • (2005) Nonlinear Dynamics , vol.41 , pp. 309-325
    • Mezić, I.1
  • 24
    • 84872255985 scopus 로고    scopus 로고
    • Analysis of fluid flows via spectral properties of the Koopman operator
    • I. Mezić, Analysis of fluid flows via spectral properties of the Koopman operator, Annual Review of Fluid Mechanics, 45 (2013), 357-378
    • (2013) Annual Review of Fluid Mechanics , vol.45 , pp. 357-378
    • Mezić, I.1
  • 27
    • 77957153107 scopus 로고    scopus 로고
    • Dynamic mode decomposition of numerical and experimental data
    • P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, Journal of Fluid Mechanics, 656 (2010), 5-28
    • (2010) Journal of Fluid Mechanics , vol.656 , pp. 5-28
    • Schmid, P.J.1
  • 28
    • 84861654467 scopus 로고    scopus 로고
    • Decomposition of time-resolved tomographic PIV
    • P. J. Schmid, D. Violato and F. Scarano, Decomposition of time-resolved tomographic PIV, Experiments in Fluids, 52 (2012), 1567-1579
    • (2012) Experiments in Fluids , vol.52 , pp. 1567-1579
    • Schmid, P.J.1    Violato, D.2    Scarano, F.3
  • 31
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures. part I: Coherent structures
    • L. Sirovich, Turbulence and the dynamics of coherent structures. part I: Coherent structures, Quarterly of applied mathematics, 45 (1987), 561-571
    • (1987) Quarterly of applied mathematics , vol.45 , pp. 561-571
    • Sirovich, L.1
  • 33
    • 84906799453 scopus 로고    scopus 로고
    • Toward compressed DMD: Spectral analysis of fluid flows using sub-Nyquist-rate PIV data
    • J. H. Tu, C. W. Rowley, J. N. Kutz and J. K. Shang, Toward compressed DMD: Spectral analysis of fluid flows using sub-Nyquist-rate PIV data, Experiments in Fluids, 55 (2014), 1-13
    • (2014) Experiments in Fluids , vol.55 , pp. 1-13
    • Tu, J.H.1    Rowley, C.W.2    Kutz, J.N.3    Shang, J.K.4
  • 35
    • 84945465279 scopus 로고    scopus 로고
    • A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition
    • M. O. Williams, I. G. Kevrekidis and C. W. Rowley, A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition, Journal of Nonlinear Science, 25 (2015), 1307-1346
    • (2015) Journal of Nonlinear Science , vol.25 , pp. 1307-1346
    • Williams, M.O.1    Kevrekidis, I.G.2    Rowley, C.W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.