Results 11 to 20 of about 179,380 (196)
Kinetically Consistent Coarse Graining Using Kernel-Based Extended Dynamic Mode Decomposition [PDF]
Journal of Chemical Theory and ComputationIn 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 ...
Vahid Nateghi, Feliks Nüske
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Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations [PDF]
Nonlinear Theory and Its Applications, IEICE, 2021 Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with the nonlinear phenomena, have been rapidly developing by incorporating machine learning methods.
Hiroaki Terao +2 more
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IEEE Control Systems Letters, 2022 Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on the quality of the particular dictionary's span, specifically on how close it is to being invariant under the ...
Masih Haseli, Jorge Cortés
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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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On Analytical Construction of Observable Functions in Extended Dynamic Mode Decomposition for Nonlinear Estimation and Prediction [PDF]
IEEE Control Systems Letters, 2020 We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of observable functions is fundamental for the application of EDMD to nonlinear problems arising in systems and control ...
Marcos Netto +3 more
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Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017 Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD)51 and its generalization, the extended-DMD (EDMD), are becoming increasingly popular in practical applications.
Qianxiao Li +3 more
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Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control [PDF]
2020 American Control Conference (ACC), 2020 This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator.
Carl Folkestad +5 more
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, 2022 This paper proposes an original methodology to compute the regions of attraction in hyperbolic and polynomial nonlinear dynamical systems using the eigenfunctions of the discrete-time approximation of the Koopman operator given by the extended dynamic mode decomposition algorithm.
Camilo Garcia-Tenorio +3 more
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Data-driven MPC with stability guarantees using extended dynamic mode decomposition [PDF]
IEEE Transactions on Automatic Control18 pages, 3 ...
Lea Bold +3 more
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Analytic Extended Dynamic Mode Decomposition [PDF]
22 ...
Alexandre Mauroy, Igor Mezić
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