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Dynamical Low-Rank Smoothing
Abstract
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.
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BibTeX
@misc{marzouk2026dynamical,
title = {{Dynamical Low-Rank Smoothing}},
author = {Youssef Marzouk and Fabio Nobile and Fabio Zoccolan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.27438},
eprint = {2607.27438},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27438},
}
RIS
TY - UNPB
TI - Dynamical Low-Rank Smoothing
AU - Youssef Marzouk
AU - Fabio Nobile
AU - Fabio Zoccolan
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.27438
UR - https://arxiv.org/abs/2607.27438
AB - 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.
ER -