Results 11 to 20 of about 6,808,722 (274)
A concise introduction to Koopman operator theory and the Extended Dynamic Mode Decomposition [PDF]
CoRR13 pages, subject introduction ...
Christophe Patyn, Geert Deconinck
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Extended dynamic mode decomposition for model reduction in fluid dynamics simulations [PDF]
Physics of FluidsHigh computational cost and storage/memory requirements of fluid dynamics simulations constrain their usefulness as a predictive tool. Reduced-order models (ROMs) provide a viable solution to this challenge by extracting the key underlying dynamics of a complex system directly from data. We investigate the efficacy and robustness of an extended dynamic
Giulia Libero +3 more
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Extended dynamic mode decomposition for two paradigms of non-linear dynamical systems
Journal of the Franklin Institute, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John Leventides +2 more
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Dictionary learning in Extended Dynamic Mode Decomposition using a reservoir computer [PDF]
, 2019 We aim at improving extended dynamic mode decomposition that allows to linearize nonlinear systems.Indeed, the EDMD algorithm provides a finite-dimensional representation of the Koopman operator.Finally, the reservoir computer is trained to produce an efficient ...
Gulina, Marvyn; id_orcid 0000-0001-6420-6911 +1 more
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Linear Control of a Nonlinear Aerospace System via Extended Dynamic Mode Decomposition
AIAA SCITECH 2022 Forum, 2022 The linear representation of nonlinear systems dynamics has a tremendous potential to enable the estimation, prediction, and control of nonlinear systems using standard and well-known methodologies available for linear systems. Numerical algorithms such as the Extended Dynamic Mode Decomposition (EDMD) has been recently proposed to identify, from ...
Cartocci, Nicholas +5 more
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$L^\infty$-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition [PDF]
CoRRExtended dynamic mode decomposition (EDMD) is a well-established method to generate a data-driven approximation of the Koopman operator for analysis and prediction of nonlinear dynamical systems. Recently, kernel EDMD (kEDMD) has gained popularity due to its ability to resolve the challenging task of choosing a suitable dictionary by using the kernel's
Frederik Köhne +4 more
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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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Koopman theory is widely used for data-driven modeling of nonlinear dynamical systems. One of the well-known algorithms that stem from this approach is the Extended Dynamic Mode Decomposition (EDMD), a data-driven algorithm for uncontrolled systems. In this thesis, we will start by discussing the EDMD algorithm.
Tilki, Cankat
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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.
europepmc +5 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 ...
Milan Korda, Igor Mezic
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