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Abstract
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]. While convergence results for EDMD require an infinite number of dictionary elements, recent studies have shown that only a few dictionary elements can yield an efficient approximation of the Koopman operator, provided that they are well-chosen through a proper training process. However, this training process typically relies on nonlinear optimization techniques. In this paper, we propose two novel methods based on a reservoir computer to train the dictionary. These methods rely solely on linear convex optimization. We illustrate the efficiency of the method with several numerical examples in the context of data reconstruction, prediction, and computation of the Koopman operator spectrum. These results pave the way for the use of the reservoir computer in the Koopman operator framework.
Original language | English |
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Article number | 023116 |
Journal | Chaos: an interdisciplinary journal of nonlinear science |
Volume | 31 |
Issue number | 2 |
DOIs | |
Publication status | Published - 9 Feb 2021 |
Keywords
- Koopman operator
- Dictionary learning
- Reservoir computing
- Nonlinear dynamics
- Dynamic mode decomposition (DMD)
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Dive into the research topics of 'Two methods to approximate the Koopman operator with a reservoir computer'. Together they form a unique fingerprint.Activities
- 3 Participation in conference
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Second Symposium on Machine Learning and Dynamical Systems
Marvyn GULINA (Contributor)
15 Sept 2020Activity: Participating in or organising an event types › Participation in conference
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Ecole Doctorale Thématique (EDT) COMPLEX
Marvyn GULINA (Contributor)
4 Feb 2020Activity: Participating in or organising an event types › Participation in conference
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Young Mathematicians Symposium of the Greater Region
Marvyn GULINA (Poster)
23 Sept 2019 → 24 Sept 2019Activity: Participating in or organising an event types › Participation in conference
Student theses
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On the approximations of the Koopman operator and applications to spectral identification of networks
Author: Gulina, M., 3 Nov 2023Supervisor: Mauroy, A. (Supervisor), Carletti, T. (Co-Supervisor), Winkin, J. (President), Hendrickx, J. (External person) (Jury) & Dietrich, F. (External person) (Jury)
Student thesis: Doc types › Doctor of Sciences
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