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 +7 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 +2 more
doaj +8 more sources
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 +9 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.
Milan Korda, Igor Mezić
core +7 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 +4 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
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
semanticscholar +6 more sources
Scalable Extended Dynamic Mode Decomposition Using Random Kernel Approximation [PDF]
SIAM Journal on 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 M. DeGennaro, Nathan M. Urban
semanticscholar +6 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
An introduction to extended dynamic mode decomposition: Estimation of the Koopman operator and outputs. [PDF]
, 2021 System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the underlying system.
Nibodh Boddupalli
+5 more sources