Results 251 to 260 of about 17,648 (273)

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 M Degennaro, Nathan M Urban
exaly   +3 more sources

Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations

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.
Hiroaki Terao, Sho Shirasaka, Hideyuki Suzuki   +2 more
exaly   +4 more sources

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Higher Order Extended Dynamic Mode Decomposition Based on the Structured Total Least Squares

SIAM Journal of Scientific Computing, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiyang Ding
exaly   +2 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 ...
Feliks Nuske, Friedrich M Philipp, Manuel Schaller   +2 more
exaly   +4 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, Yoshihiko Susuki, Venkat Krishnan   +2 more
exaly   +3 more sources

Koopman operators and Extended dynamic mode decomposition for the inverted pendulum

2022 4th International Conference on Industrial Artificial Intelligence (IAI), 2022
John Leventides, Evangelos Melas, Costas Poulios   +2 more
exaly   +2 more sources

Symbolic extended dynamic mode decomposition

Chaos: An Interdisciplinary Journal of Nonlinear Science
In this paper, we present a new method of performing extended dynamic mode decomposition (EDMD) on systems, which admit a symbolic representation. EDMD generates estimates of the Koopman operator, K, for a dynamical system by defining a dictionary of observables on the space and producing an estimate, Km, which is restricted to be invariant on the span
Connor Kennedy, John Kaushagen, Hong-Kun Zhang   +2 more
openaire   +3 more sources

Temporal Forward–Backward Consistency, Not Residual Error, Measures the Prediction Accuracy of Extended Dynamic Mode Decomposition

IEEE Control Systems Letters, 2023
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on the quality of the particular dictionary's span, specifically on how close it is to being invariant under the ...
Masih Haseli, Jorge Cortes
exaly   +3 more sources

Extended Dynamic Mode Decomposition with Invertible Dictionary Learning

Neural Networks
The Koopman operator has received attention for providing a potentially global linearization representation of the nonlinear dynamical system. To estimate or control the original system, the invertibility problem is introduced into the data-driven modeling, i.e., the observables are required to be reconstructed the original system's states.
Yuhong Jin, Lei Hou, Shun Zhong
openaire   +2 more sources

Dimension of Lift and Numerical Stability in Extended Dynamic Mode Decomposition

2025 SICE International Symposium on Control Systems (SICE ISCS)
Kenji Uchiyama, Kai Masuda
exaly   +2 more sources