Dynamical Low-Rank Smoothing
arXiv:2607.27438
The paper introduces a dynamical low-rank approximation framework to create efficient reduced-order smoothers for high-dimensional stochastic differential equation models, extending joint mean-and-covariance optimization filtering to the Rauch‑Tung‑Striebel and Kalman‑Bucy smoothing recursions.
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.
11 pages