Featurizing Koopman Mode Decomposition For Robust Forecasting
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909283360178176 |
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| author | Aristoff, David Copperman, Jeremy Mankovich, Nathan Davies, Alexander |
| author_facet | Aristoff, David Copperman, Jeremy Mankovich, Nathan Davies, Alexander |
| contents | This article introduces an advanced Koopman mode decomposition (KMD) technique -- coined Featurized Koopman Mode Decomposition (FKMD) -- that uses delay embedding and a learned Mahalanobis distance to enhance analysis and prediction of high dimensional dynamical systems. The delay embedding expands the observation space to better capture underlying manifold structure, while the Mahalanobis distance adjusts observations based on the system's dynamics. This aids in featurizing KMD in cases where good features are not a priori known. We show that FKMD improves predictions for a high-dimensional linear oscillator, a high-dimensional Lorenz attractor that is partially observed, and a cell signaling problem from cancer research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09146 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Featurizing Koopman Mode Decomposition For Robust Forecasting Aristoff, David Copperman, Jeremy Mankovich, Nathan Davies, Alexander Dynamical Systems Mathematical Physics Machine Learning 37M22, 37M05, 37M10, 37M15, 37N25 This article introduces an advanced Koopman mode decomposition (KMD) technique -- coined Featurized Koopman Mode Decomposition (FKMD) -- that uses delay embedding and a learned Mahalanobis distance to enhance analysis and prediction of high dimensional dynamical systems. The delay embedding expands the observation space to better capture underlying manifold structure, while the Mahalanobis distance adjusts observations based on the system's dynamics. This aids in featurizing KMD in cases where good features are not a priori known. We show that FKMD improves predictions for a high-dimensional linear oscillator, a high-dimensional Lorenz attractor that is partially observed, and a cell signaling problem from cancer research. |
| title | Featurizing Koopman Mode Decomposition For Robust Forecasting |
| topic | Dynamical Systems Mathematical Physics Machine Learning 37M22, 37M05, 37M10, 37M15, 37N25 |
| url | https://arxiv.org/abs/2312.09146 |