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Fabio Zoccolan

Publications and source records attributed to Fabio Zoccolan.

2 recordsLinked to original sources
arXiv2026

Dynamical Low-Rank Filters for Data Assimilation

We propose dynamical low-rank (DLR) type filters for data-assimilation problems based on stochastic differential equations (SDEs). In detail, first we derive a DLRA filter for minimizing jointly the mean and covariance error, as well as a strategy to efficiently include the relevant orthogonal directions. This last approach allows the main subspace to evolve also according to the observation operator. Those procedures naturally extend to a Kalman-Bucy type filter when dealing with linear drift, and to ensemble methods, too, resulting also suitable for problems described by nonlinear drift and possible non-Gaussian distribution. Moreover, we further propose a preliminary particle-type DLRA filter that shows potentiality in nonlinear settings. Numerical simulations show the efficacy of these procedures in relevant applications, opening up to further studies in these filtering directions.

math.NA↗
arXiv2026

Dynamical Low-Rank Smoothing

Computational costs often make smoothing procedures prohibitive for high-dimensional data assimilation problems. To address this challenge, we propose a dynamical low-rank approximation (DLRA) methodology for smoothing concerning frameworks based on stochastic differential equations. We extend the previously developed joint mean-and-covariance optimization (JMCO) filtering setting to derive a reduced-order smoother via the Rauch--Tung--Striebel recursion and establish the corresponding Kalman--Bucy smoothing for affine drift dynamics. The resulting algorithms retain the adaptive nature of DLRA while significantly reducing the computational time and storage of the whole smoothing procedure.

math.NA↗