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Scalable Extended Dynamic Mode Decomposition Using Random Kernel Approximation [PDF]
SIAM Journal of 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 DeGennaro
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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, 2021 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 +2 more
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Orthogonal Polynomial Approximation and Extended Dynamic Mode Decomposition in Chaos
SIAM Journal on Numerical AnalysisExtended Dynamic Mode Decomposition (EDMD) is a data-driven tool for forecasting and model reduction of dynamics, which has been extensively taken up in the physical sciences. While the method is conceptually simple, in deterministic chaos it is unclear what its properties are or even what it converges to.
Caroline L Wormell
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Higher Order Extended Dynamic Mode Decomposition Based on the Structured Total Least Squares
SIAM Journal of Scientific Computing, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiyang Ding, Jie Li
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Symbolic extended dynamic mode decomposition
Chaos: An Interdisciplinary Journal of Nonlinear ScienceIn this paper, we present a new method of performing extended dynamic mode decomposition (EDMD) on systems, which admit a symbolic representation. EDMD generates estimates of the Koopman operator, K, for a dynamical system by defining a dictionary of observables on the space and producing an estimate, Km, which is restricted to be invariant on the span
Connor Kennedy +2 more
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IEEE Control Systems Letters, 2023 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 ...
Jorge Cortés, Masih Haseli
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Extended Dynamic Mode Decomposition with Invertible Dictionary Learning
Neural NetworksThe Koopman operator has received attention for providing a potentially global linearization representation of the nonlinear dynamical system. To estimate or control the original system, the invertibility problem is introduced into the data-driven modeling, i.e., the observables are required to be reconstructed the original system's states.
Yuhong Jin, Lei Hou, Shun Zhong
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Weak-form Extended Dynamic Mode Decomposition
In this work, we develop a weak-form version of Extended Dynamic Mode Decomposition that we call WEDMD. We establish a number of analytic results about the method and show explicitly how the weak form is able to mitigate the impacts of noise in linear stochastic differential equations.Curtis, Christopher W., Bortz, David M.
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2019 American Control Conference (ACC), 2019
This paper presents a data-driven method to find a finite-dimensional approximation for the Koopman operator using noisy data. The proposed method is a modification of Extended Dynamic Mode Decomposition which finds an approximation for the projection of the Koopman operator on a subspace spanned by a predefined dictionary of functions.
Jorge Cortés, Masih Haseli
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This paper presents a data-driven method to find a finite-dimensional approximation for the Koopman operator using noisy data. The proposed method is a modification of Extended Dynamic Mode Decomposition which finds an approximation for the projection of the Koopman operator on a subspace spanned by a predefined dictionary of functions.
Jorge Cortés, Masih Haseli
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SIAM Journal on Applied Dynamical Systems. We prove [Formula: see text]-error bounds for kernel extended dynamic mode decomposition (kEDMD) approximants of the Koopman operator for stochastic dynamical systems.
Karl Worthmann +2 more
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