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SUMMARY:Dynamical Low-Rank Kalman Filtering - Thomas Trigo trindade (EPFL 
 - Ecole Polytechnique Fédérale de Lausanne)
DTSTART:20250507T130000Z
DTEND:20250507T133000Z
UID:TALK230500@talks.cam.ac.uk
DESCRIPTION:Data Assimilation consists in combining one's model knowledge 
 with a stream of data in order to improve the prediction of the system sta
 te. Two successful outlets of that approach are given by the Kalman-Bucy f
 ilter and its particle-based analog\, the Ensemble Kalman filter. While th
 e former describes the exact filtering density evolution in the case of li
 near and Gaussian dynamics\, in practice the latter is often used in real-
 world applications such as climate or geosciences\, as it is computational
 ly tractable. Despite the intrinsic low-rank structure many real-life syst
 ems seem to present\, using a small number of particles might lead to sign
 ificant Monte-Carlo error and stochastic fluctuations. We propose a princi
 pled model order reduction of the Kalman-Bucy filter (KBF) by way of the D
 ynamical Low-Rank (DLR) Approximation method\, mimicking a time-evolving t
 runcated Karhunen-Loeven approximation of the filtering density. In essenc
 e\, leveraging the low-rank structure of the filtering density allows to e
 volve (an approximation of) it in a dynamically evolving subspace\, at red
 uced computational cost. Under certain assumptions\, our framework preserv
 es well-known properties of the KBF (including mean and covariance charact
 erisation)\, and we also establish error bounds between the true and reduc
 ed order model. We also propose a DLR extension of the Ensemble Kalman fil
 ter\, and show a propagation of chaos property to its rank-reduced mean-fi
 eld limit.
LOCATION:Seminar Room 1\, Newton Institute
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