Results 1 to 10 of about 17,378 (151)

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, Bertrand Chapron, Fabrice Collard, Lucile Gaultier, Ronan Fablet   +4 more
doaj   +4 more sources

Evaluation of the Regions of Attraction of Higher-Dimensional Hyperbolic Systems Using Extended Dynamic Mode Decomposition

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, Duvan Tellez-Castro, Eduardo Mojica-Nava, Alain Vande Wouwer   +3 more
doaj   +3 more sources

A Matlab Toolbox for Extended Dynamic Mode Decomposition Based on Orthogonal Polynomials and p-q Quasi-Norm Order Reduction

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, Alain Vande Wouwer   +1 more
doaj   +3 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. Assuming that the samples are drawn either independently or ergodically from some measure $μ$, it was shown that, in the limit as $M ...
Igor Mezic, Milan Korda, Mezic Igor
exaly   +4 more sources

Trigonometric Embeddings in Polynomial Extended Mode Decomposition—Experimental Application to an Inverted Pendulum

Mathematics, 2021
The extended dynamic mode decomposition algorithm is a tool for accurately approximating the point spectrum of the Koopman operator. This algorithm provides an approximate linear expansion of non-linear discrete-time systems, which can be useful for ...
Camilo Garcia-Tenorio, Gilles Delansnay, Eduardo Mojica-Nava, Alain Vande Wouwer   +3 more
doaj   +3 more sources

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
exaly   +3 more sources

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, Hisaichi Shibata, Ryoji Takaki   +2 more
doaj   +5 more sources

Kinetically Consistent Coarse Graining Using Kernel-Based Extended Dynamic Mode Decomposition. [PDF]

J Chem Theory Comput
In 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.
europepmc   +5 more sources

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, Yingchen Zhang, Venkat Krishnan   +2 more
exaly   +3 more sources

Group-convolutional extended dynamic mode decomposition

Physica D: Nonlinear Phenomena
This 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 ...
Karl Worthmann, Feliks Nuske, Friedrich Philipp   +2 more
exaly   +4 more sources