A competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering
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| Format: | Preprint |
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2024
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| author | Malik, Zachariah Maulik, Romit |
| author_facet | Malik, Zachariah Maulik, Romit |
| contents | Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications. However, the vanilla EnKF framework is not well-defined when perturbations are nonlinear. We study two non-linear extensions of the vanilla EnKF - dubbed the conditional-Gaussian EnKF (CG-EnKF) and the normal score EnKF (NS-EnKF) - which sidestep assumptions of linearity by constructing the Kalman gain matrix with the `conditional Gaussian' update formula in place of the traditional one. We then compare these models against a state-of-the-art deep learning based particle filter called the score filter (SF). This model uses an expensive score diffusion model for estimating densities and also requires a strong assumption on the perturbation operator for validity. In our comparison, we find that CG-EnKF and NS-EnKF dramatically outperform SF for a canonical problem in high-dimensional multiscale data assimilation given by the Lorenz-96 system. Our analysis also demonstrates that the CG-EnKF and NS-EnKF can handle highly non-Gaussian additive noise perturbations, with the latter typically outperforming the former. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_14300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering Malik, Zachariah Maulik, Romit Machine Learning Dynamical Systems Atmospheric and Oceanic Physics Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications. However, the vanilla EnKF framework is not well-defined when perturbations are nonlinear. We study two non-linear extensions of the vanilla EnKF - dubbed the conditional-Gaussian EnKF (CG-EnKF) and the normal score EnKF (NS-EnKF) - which sidestep assumptions of linearity by constructing the Kalman gain matrix with the `conditional Gaussian' update formula in place of the traditional one. We then compare these models against a state-of-the-art deep learning based particle filter called the score filter (SF). This model uses an expensive score diffusion model for estimating densities and also requires a strong assumption on the perturbation operator for validity. In our comparison, we find that CG-EnKF and NS-EnKF dramatically outperform SF for a canonical problem in high-dimensional multiscale data assimilation given by the Lorenz-96 system. Our analysis also demonstrates that the CG-EnKF and NS-EnKF can handle highly non-Gaussian additive noise perturbations, with the latter typically outperforming the former. |
| title | A competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering |
| topic | Machine Learning Dynamical Systems Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2409.14300 |