Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework [PDF]
Machine Learning: Science and Technology, 2023 Bernard O Koopman proposed an alternative view of dynamical systems based on linear operator theory, in which the time evolution of a dynamical system is analogous to the linear propagation of an infinite-dimensional vector of observables.
Said Ouala +4 more
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Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising. [PDF]
PLoS ONE, 2019 A new dynamic mode decomposition (DMD) method is introduced for simultaneous system identification and denoising in conjunction with the adoption of an extended Kalman filter algorithm.
Taku Nonomura +2 more
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Kinetically Consistent Coarse Graining Using Kernel-Based Extended Dynamic Mode Decomposition. [PDF]
J Chem Theory ComputIn this paper, we show how kernel-based models for the Koopman generator -- the gEDMD method -- can be used to identify coarse-grained dynamics on reduced variables, which retain the slowest transition timescales of the original dynamics. The centerpiece of this study is a learning method to identify an effective diffusion in coarse-grained space ...
Nateghi V, Nüske F.
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Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition [PDF]
Automation, 2023 This paper provides the theoretical foundation for the approximation of the regions of attraction in hyperbolic and polynomial systems based on the eigenfunctions deduced from the data-driven approximation of the Koopman operator.
Camilo Garcia-Tenorio +3 more
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A Matlab Toolbox for Extended Dynamic Mode Decomposition Based on Orthogonal Polynomials and p-q Quasi-Norm Order Reduction [PDF]
Mathematics, 2022 Extended Dynamic Mode Decomposition (EDMD) allows an approximation of the Koopman operator to be derived in the form of a truncated (finite dimensional) linear operator in a lifted space of (nonlinear) observable functions.
Camilo Garcia-Tenorio +1 more
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IEEE AccessThis paper presents a novel framework for adaptive learning of Koopman operator to predict the behavior of nonlinear time-varying dynamical systems based on the celebrated extended dynamic mode decomposition (EDMD).
Reiya Asuke, Masahiro Yukawa
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Extended dynamic mode decomposition for inhomogeneous problems [PDF]
Journal of Computational Physics, 2021 Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for systems described by partial differential equations (PDEs) with homogeneous boundary conditions.
Hannah Lu, Daniel M. Tartakovsky
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An introduction to extended dynamic mode decomposition: Estimation of the Koopman operator and outputs. [PDF]
, 2021 System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the underlying system.
Nibodh Boddupalli
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Scalable Extended Dynamic Mode Decomposition Using Random Kernel Approximation [PDF]
SIAM Journal on Scientific Computing, 2019 The Koopman operator is a linear, infinite-dimensional operator that governs the dynamics of system observables; Extended Dynamic Mode Decomposition (EDMD) is a data-driven method for approximating the Koopman operator using functions (features) of the system state snapshots.
Anthony M. DeGennaro, Nathan M. Urban
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AIP AdvancesTo enhance the accuracy and efficiency of transient temperature rise and hot-spot temperature calculations for oil-immersed transformer windings, this study proposes an extended dynamic mode decomposition computational strategy.
Kexin Liu +6 more
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