Results 51 to 60 of about 1,063,107 (310)
Extending the extended dynamic mode decomposition with latent observables: the latent EDMD framework
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
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Mathematics, 2021 Inferring the latent structure of complex nonlinear dynamical systems in a data driven setting is a challenging mathematical problem with an ever increasing spectrum of applications in sciences and engineering.
Zlatko Drmač, Igor Mezić, Ryan Mohr
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PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator [PDF]
Journal of Open Source Software, 2023 PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction, estimation, and ...
Shaowu Pan +4 more
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On the Approximability of Koopman-Based Operator Lyapunov Equations
SIAM Journal on Control and Optimization, 2023 Lyapunov equations, Koopman operator, infinite dimensional systems ...
Breiten, Tobias, Höveler, Bernhard
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Delay-Coordinate Maps and the Spectra of Koopman Operators [PDF]
Journal of Statistical Physics, 2019 The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting. Koopman eigenfunctions represent the non-mixing component of the dynamics. They factor the dynamics, which can be chaotic, into quasiperiodic rotations on
Suddhasattwa Das, Dimitrios Giannakis
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Linear identification of nonlinear systems: A lifting technique based on the Koopman operator [PDF]
, 2016 We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification ...
Goncalves, Jorge, Mauroy, Alexandre
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Learning Koopman Operator under Dissipativity Constraints
IFAC-PapersOnLine, 2020 This paper addresses a learning problem for nonlinear dynamical systems with incorporating any specified dissipativity property. The nonlinear systems are described by the Koopman operator, which is a linear operator defined on the infinite-dimensional lifted state space.
Noboru Sebe, Masaki Inoue, Keita Hara
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Two methods to approximate the Koopman operator with a reservoir computer [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2021 The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, a wealth of numerical methods providing finite-dimensional approximations of the operator have been proposed [e.g., extended dynamic mode decomposition (EDMD) and its variants].
Marvyn Gulina, Alexandre Mauroy
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Data-Driven Congestion Control of Micro Smart Sensor Networks for Transparent Substations
IEEE Access, 2021 Micro smart sensors and sensor networks are the key bases for building a fully visible, perceptible and controllable transparent substation in power grid.
Ke Zhou +3 more
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Deep Koopman Operator-Informed Safety Command Governor for Autonomous Vehicles [PDF]
IEEE/ASME transactions on mechatronicsModeling of nonlinear behaviors with physical-based models poses challenges. However, Koopman operator maps the original nonlinear system into an infinite-dimensional linear space to achieve global linearization of the nonlinear system through input and ...
Hao Chen +3 more
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