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
doaj +8 more sources
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
doaj +3 more sources
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
doaj +6 more sources
Extended dynamic mode decomposition for cyclic macroeconomic data
Data Science in Finance and Economics, 2022 We apply methods from the Koopman operator theory, Extended Dynamic Mode Decomposition and machine learning in the study of business cycle models. We use a simple non-linear dynamical system whose main merit is that in the appropriate parameter space ...
John Leventides +2 more
doaj +3 more sources
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
doaj +3 more sources
A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition [PDF]
Journal of Nonlinear Science, 2015 The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of nonlinear ...
Matthew O. Williams +2 more
core +6 more sources
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator [PDF]
Journal of Nonlinear Science, 2017 Extended Dynamic Mode Decomposition (EDMD) is an algorithm that approximates the action of the Koopman operator on an $N$-dimensional subspace of the space of observables by sampling at $M$ points in the state space.
Korda, Milan, Mezić, Igor
core +4 more sources
On the Effect of Quantization on Extended Dynamic Mode Decomposition [PDF]
2025 American Control Conference (ACC)Extended Dynamic Mode Decomposition (EDMD) is a widely used data-driven algorithm for estimating the Koopman Operator. EDMD extends Dynamic Mode Decomposition (DMD) by lifting the snapshot data using nonlinear dictionary functions before performing the estimation.
Dilip Kumar Maity, Debdipta Goswami
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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
openalex +4 more sources
Group-convolutional extended dynamic mode decomposition [PDF]
Physica D: Nonlinear PhenomenaThis paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach. Approximating the Koopman operator by finite-dimensional surrogates, e.g., via extended dynamic mode decomposition (EDMD), is challenging for high ...
H. Harder +5 more
+5 more sources