Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations
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- Terao Hiroaki
- Graduate School of Information Science and Technology, Osaka University
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- Shirasaka Sho
- Graduate School of Information Science and Technology, Osaka University
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- Suzuki Hideyuki
- Graduate School of Information Science and Technology, Osaka University
Abstract
<p>Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with the nonlinear phenomena, have been rapidly developing by incorporating machine learning methods. Neural ordinary differential equations (NODEs), which are a neural network equipped with a continuum of layers, and have high parameter and memory efficiencies, have been proposed. In this paper, we propose an algorithm to perform EDMD using NODEs. NODEs are used to find a parameter-efficient dictionary which provides a good finite-dimensional approximation of the Koopman operator. We show the superiority of the parameter efficiency of the proposed method through numerical experiments.</p>
Journal
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- Nonlinear Theory and Its Applications, IEICE
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Nonlinear Theory and Its Applications, IEICE 12 (4), 626-638, 2021
The Institute of Electronics, Information and Communication Engineers
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Keywords
Details 詳細情報について
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- CRID
- 1390008089765247232
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- NII Article ID
- 130008098006
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- ISSN
- 21854106
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed