Results 31 to 40 of about 472,452 (242)
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 $η$ and $δ$, as well as ratios of critical exponents, of classical spin systems from single observables alone.
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Uncertainty Quantification of Autoencoder-based Koopman Operator [PDF]
, 2023 This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state.
Quan, Ying Shuai +2 more
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A Koopman Operator Tutorial with Othogonal Polynomials
CoRR, 2021 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 eigenfunctions of the system.
Simone Servadio +2 more
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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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Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control. [PDF]
PLoS ONE, 2016 In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions.
Steven L Brunton +3 more
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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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Diffeomorphically Learning Stable Koopman Operators
IEEE Control Systems Letters, 2022 Revised version submitted to IEEE Control Systems Letters (L-CSS) with substantially revised exposition, evaluation and proof of Lemma 2 (previously Lemma 8)
Petar Bevanda +5 more
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Feedback Stabilization Using Koopman Operator [PDF]
2018 IEEE Conference on Decision and Control (CDC), 2018 Accepted for IEEE Conference on Decision and Control(CDC ...
Bowen Huang, Xu Ma 0002, Umesh Vaidya
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Koopman Operator Framework for Spectral Analysis and Identification of Infinite-Dimensional Systems
Mathematics, 2021 We consider the Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a finite-dimensional
Alexandre Mauroy
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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 ...
Tobias Breiten, Bernhard Höveler
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