| Autor: |
Neranjaka Jayarathne, Erik M. Bollt |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 9, Iss 1, Pp 998-1022 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2024050?viewType=HTML |
| Popis: |
Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through the Koopman operator(KO) analysis. However, computing Koopman eigenpairs for high-dimensional observable data can be inefficient. This paper proposes using deep autoencoders(AE), a type of deep learning technique, to perform nonlinear geometric transformations on raw data before computing Koopman eigenvectors. The encoded data produced by the deep AE is diffeomorphic to a manifold of the dynamical system and has a significantly lower dimension than the raw data. To handle high-dimensional time series data, Takens' time delay embedding is presented as a preprocessing technique. The paper concludes by presenting examples of these techniques in action. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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