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This paper presents the Ensemble Schrödinger Bridge filter, a derivative-free and training-free nonlinear optimal filtering method designed to handle highly complex dynamics without structural model error. By integrating diffusion-generative-modeling into standard prediction steps, it achieves superior performance over classical filters like the ensemble Kalman filter even in high-dimensional chaotic systems up to 40 dimensions. The approach highlights significant potential for advancing data assimilation tasks where traditional linear approximations fail, with future applications targeting practical meteorological modeling.
The Ensemble Schr{\"o}dinger Bridge filter for Nonlinear Data Assimilation
arXiv:2512.18928v4 Announce Type: replace Abstract: This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{\"o}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis step, thereby completing one full filtering update. The resulting approach introduces no structural model error, and is derivative-free, training-free, and highly parallelizable. Numerical experiments demonstrate that the proposed algorithm performs effectively for highly nonlinear dynamics and nonlinear observation processes, including chaotic systems with dimension up to 40 and beyond. The results also show that the method outperforms classical approaches such as the ensemble Kalman filter and particle filter across a range of tests with varying degrees of nonlinearity. Future work will focus on extending the proposed method to practical meteorological applications and developing a rigorous convergence theory.
Abstract:This work introduces a novel nonlinear optimal filtering method, termed the Ensemble Schr{ö}dinger Bridge nonlinear filter. The proposed filter combines the standard prediction step with a diffusion-generative-modeling-based analysis step, thereby completing one full filtering update. The resulting approach introduces no structural model error, and is derivative-free, training-free, and highly parallelizable. Numerical experiments demonstrate that the proposed algorithm performs effectively for highly nonlinear dynamics and nonlinear observation processes, including chaotic systems with dimension up to 40 and beyond. The results also show that the method outperforms classical approaches such as the ensemble Kalman filter and particle filter across a range of tests with varying degrees of nonlinearity. Future work will focus on extending the proposed method to practical meteorological applications and developing a rigorous convergence theory.
Machine Learning (cs.LG)
arXiv:2512.18928 [cs.LG]
(or arXiv:2512.18928v4 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2512.18928 Focus to learn more arXiv-issued DOI via DataCite
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