Results 11 to 20 of about 17,477 (250)
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.
Sho Shirasaka +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 Wormell
exaly +3 more sources
On the Effect of Quantization on Extended Dynamic Mode Decomposition
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.
Debdipta Goswami, Dipankar Maity
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Data-Driven MPC With Stability Guarantees Using Extended Dynamic Mode Decomposition
IEEE Transactions on Automatic Control18 pages, 3 ...
Karl Worthmann +2 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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Efficient Nonlinear Model Predictive Control of Automated Vehicles
Mathematics, 2022 In this paper, an efficient model predictive control (MPC) of velocity tracking of automated vehicles is proposed, in which a reference signal is given a priori.
Shuyou Yu +5 more
doaj +1 more source
Extended dynamic mode decomposition for cyclic macroeconomic data
Data Science in Finance and Economics, 2022 <abstract><p>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 sector predicts intrinsically business cycles which in the phase space are ...
John Leventides +2 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.
Folkestad, Carl +5 more
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Analysis of the ROA of an anaerobic digestion process via data-driven Koopman operator
Nonlinear Engineering, 2021 Nonlinear biochemical systems such as the anaerobic digestion process experience the problem of the multi-stability phenomena, and thus, the dynamic spectrum of the system has several undesired equilibrium states.
Garcia-Tenorio Camilo +3 more
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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 dynamical systems.
Matthew O. Williams +2 more
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