Dynamical systems and complex networks: A Koopman operator perspective
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915064601116672 |
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| author | Klus, Stefan Conrad, Nataša Djurdjevac |
| author_facet | Klus, Stefan Conrad, Nataša Djurdjevac |
| contents | The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear operators$\unicode{x2013}$has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical systems and complex networks: A Koopman operator perspective Klus, Stefan Conrad, Nataša Djurdjevac Dynamical Systems Machine Learning The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear operators$\unicode{x2013}$has been known for a long time, the availability of large data sets and efficient machine learning algorithms for estimating the Koopman operator from data make this framework extremely powerful and popular. Koopman operator theory allows us to gain insights into the characteristic global properties of a system without requiring detailed mathematical models. We will show how these methods can also be used to analyze complex networks and highlight relationships between Koopman operators and graph Laplacians. |
| title | Dynamical systems and complex networks: A Koopman operator perspective |
| topic | Dynamical Systems Machine Learning |
| url | https://arxiv.org/abs/2405.08940 |