Koopman Reduced Order Modeling with Confidence Bounds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912297811705856 |
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| author | Mohr, Ryan Fonoberova, Maria Mezic, Igor |
| author_facet | Mohr, Ryan Fonoberova, Maria Mezic, Igor |
| contents | This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spectral decomposition of the Koopman operator. The reduced order model is constructed using a finite number of Koopman eigenvalues and modes, while the rest of spectrum is treated as a noise process. This noise process is used to extract the confidence bounds. Additionally, we propose a heuristic algorithm to choose the number of deterministic modes to keep in the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13127 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Koopman Reduced Order Modeling with Confidence Bounds Mohr, Ryan Fonoberova, Maria Mezic, Igor Dynamical Systems 47B33, 15A18, 62F25, 62M20 This paper introduces a reduced order modeling technique based on Koopman operator theory that gives confidence bounds on the model's predictions. It is based on a data-driven spectral decomposition of the Koopman operator. The reduced order model is constructed using a finite number of Koopman eigenvalues and modes, while the rest of spectrum is treated as a noise process. This noise process is used to extract the confidence bounds. Additionally, we propose a heuristic algorithm to choose the number of deterministic modes to keep in the model. |
| title | Koopman Reduced Order Modeling with Confidence Bounds |
| topic | Dynamical Systems 47B33, 15A18, 62F25, 62M20 |
| url | https://arxiv.org/abs/2209.13127 |