Results 11 to 20 of about 1,745 (187)
A Koopman Operator Tutorial with Othogonal Polynomials
CoRR, 2022 The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear combination of the ...
Linares, Richard +2 more
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The Koopman Operator in Systems and Control:Concepts, Methodologies, and Applications
, 2020 This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of ...
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Koopman operator and its approximations for systems with symmetries [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019 Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, often described by complex attractor-basin portraits and enhanced and suppressed bifurcations.
Jeffrey Emenheiser +9 more
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On the approximability of Koopman-based operator Lyapunov equations
SIAM Journal on Control and Optimization, 2023 Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws such as the ...
Breiten, Tobias, Höveler, Bernhard
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Temporally consistent Koopman autoencoders for forecasting dynamical systems [PDF]
Scientific ReportsAbsence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems.
Indranil Nayak +4 more
doaj +2 more sources
Koopman operator learning using invertible neural networks
Journal of Computational PhysicsIn Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions.
Jianguo Huang, Yue Qiu
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Error bounds for kernel-based approximations of the Koopman operator [PDF]
Applied and Computational Harmonic AnalysisWe consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations.
Friedrich M Philipp +2 more
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Deep Koopman Operator-based degradation modelling
Reliability Engineering and System SafetyDeveloping reliable health indicators for industrial assets is essential for accurate condition monitoring, fault detection, and predicting the remaining useful lifetime.
Olga Fink, Sergei Garmaev
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On the Koopman Operator of Algorithms [PDF]
SIAM Journal on Applied Dynamical Systems, 2020 27 pages, 11 ...
Felix Dietrich +2 more
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Koopman Operators and the $3x+1$-Dynamical System [PDF]
SIAM Journal on Applied Dynamical Systems, 2021 The $3x+1$-problem (or Collatz problem) is a notorious conjecture in arithmetic. It can be viewed as iterating a map and, therefore, it is a dynamical system on the discrete space $\mathbb{N}$ of natural numbers. The emerging dynamical system is studied in the present work with methods from the theory of Koopman operators and $C^*$-algebras.
John Leventides, Costas Poulios
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