Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910218792730624 |
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| author | Tilki, Cankat Gugercin, Serkan |
| author_facet | Tilki, Cankat Gugercin, Serkan |
| contents | We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eigenfunctions of the Koopman semigroup when this semigroup is considered over the Banach space of continuous functions on a compact forward-invariant set endowed with the supremum norm. We then construct closed-form expressions of the action of the Koopman semigroup and its resolvent in terms of these observables. To approximate the action of Koopman semigroup numerically, we combine Extended Dynamic Mode Decomposition (EDMD) with the proposed wavelet-based observables leading to the Wavelet Dynamic Mode Decomposition via Continuous Wavelet Transform (cWDMD) algorithm. We validate our theoretical results on two numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14224 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework Tilki, Cankat Gugercin, Serkan Numerical Analysis Artificial Intelligence Dynamical Systems Functional Analysis 37M05, 37M10, 37N30, 47A15, 47A58, 47A70, 47A75 We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eigenfunctions of the Koopman semigroup when this semigroup is considered over the Banach space of continuous functions on a compact forward-invariant set endowed with the supremum norm. We then construct closed-form expressions of the action of the Koopman semigroup and its resolvent in terms of these observables. To approximate the action of Koopman semigroup numerically, we combine Extended Dynamic Mode Decomposition (EDMD) with the proposed wavelet-based observables leading to the Wavelet Dynamic Mode Decomposition via Continuous Wavelet Transform (cWDMD) algorithm. We validate our theoretical results on two numerical examples. |
| title | Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework |
| topic | Numerical Analysis Artificial Intelligence Dynamical Systems Functional Analysis 37M05, 37M10, 37N30, 47A15, 47A58, 47A70, 47A75 |
| url | https://arxiv.org/abs/2605.14224 |