Results 21 to 30 of about 1,063,107 (310)
Mathematical Modelling and Numerical Simulation with ApplicationsPoincaré's geometric representation, while historically fundamental in dynamical system analysis, faces challenges with high-dimensional and uncertain systems in modern engineering and data analysis.
Ramen Ghosh, Marion Mcafee
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Approximation of the Koopman operator via Bernstein polynomials
Communications in Nonlinear Science and Numerical SimulationThe Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional approximation methods and characterize the related approximation errors with upper bounds, preferably expressed in
Rishikesh Yadav, A. Mauroy
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Autoencoding for the "Good Dictionary" of eigenpairs of the Koopman operator
AIMS MathematicsReduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through the Koopman operator(KO) analysis.
Neranjaka Jayarathne, Erik M. Bollt
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Symplectic Geometry of the Koopman Operator [PDF]
Doklady Mathematics, 2021 Abstract We consider the Koopman operator generated by an invertible transformation of a space with a finite countably additive measure. If the square of this transformation is ergodic, then the orthogonal Koopman operator is a symplectic transformation on the real Hilbert space of square summable functions with zero ...
Valery V. Kozlov, Valery V. Kozlov
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Glocal Hypergradient Estimation with Koopman Operator
arXiv.orgGradient-based hyperparameter optimization methods update hyperparameters using hypergradients, gradients of a meta criterion with respect to hyperparameters.
Ryuichiro Hataya, Yoshinobu Kawahara
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Model-Free Geometric Fault Detection and Isolation for Nonlinear Systems Using Koopman Operator
IEEE Access, 2022 This paper presents a model-free fault detection and isolation (FDI) method for nonlinear dynamical systems using Koopman operator theory and linear geometric technique.
Mohammadhosein Bakhtiaridoust +3 more
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Measurement + Control, 2022 Omnidirectional mobile manipulators (OMMs) have been widely used due to their high mobility and operating flexibility. However, since OMMs are complex nonlinear systems with uncertainties, the dynamic modeling and control are always challenging problems.
Xuehong Zhu +3 more
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Renormalization group as a Koopman operator [PDF]
Physical Review E, 2020 Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $ $ and $ $, as well as ratios of critical exponents, of classical spin systems from single observables alone.
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Energy and AI, 2023 In this study, a novel application of the Koopman operator for control-oriented modeling of proton exchange membrane fuel cell (PEMFC) stacks is proposed. The primary contributions of this paper are: (1) the design of Koopman-based models for a fuel cell
Da Huo, Carrie M. Hall
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A quantitative analysis of Koopman operator methods for system identification and predictions
Comptes Rendus. Mécanique, 2022 We give convergence and cost estimates for a data-driven system identification method: given an unknown dynamical system, the aim is to recover its vector field and its flow from trajectory data.
Zhang, Christophe, Zuazua, Enrique
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