Dynamical Low-Rank Filters for Data Assimilation
Abstract
We propose dynamical low-rank (DLRA) filters for data-assimilation problems based on stochastic differential equations (SDEs). We first consider a Kalman filter applied to a Euler-Maruyama discretization of the SDE and observation processes, and derive a DLRA Kalman-type filter, named DLRA-JMCO, by minimizing jointly the error on the mean and covariance. We then obtain a time continuous DLRA-JMCO filter as the continuous limit of the time discrete one, and introduce a corresponding particle approximation. We also propose a strategy to enrich the DLRA-JMCO filter with a simple Gaussian process to capture the neglected dynamics in the orthogonal to the DLRA subspace. This correcting term allows the DLRA subspace evolution to be directly influenced by the observation operator. We finally propose a particle filter version of the DLRA-JMCO filter. Numerical experiments assess the performance of the proposed filters.
Related
- On the Oja-Flow-Based Low-Rank Approximation of Kalman-Bucy Filters for Linear Time-Varying Systems
- Defense Filters for Robust Learning of Partially Observed Dynamical Systems
- Dynamical Low-Rank Smoothing
- Further Approaches of Dynamical Low-Rank Approximation for SDEs
- Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients
BibTeX
@misc{kazashi2026dynamical,
title = {{Dynamical Low-Rank Filters for Data Assimilation}},
author = {Yoshihito Kazashi and Youssef Marzouk and Fabio Nobile and Fabio Zoccolan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.27432},
eprint = {2607.27432},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27432},
}
RIS
TY - UNPB
TI - Dynamical Low-Rank Filters for Data Assimilation
AU - Yoshihito Kazashi
AU - Youssef Marzouk
AU - Fabio Nobile
AU - Fabio Zoccolan
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2607.27432
UR - https://arxiv.org/abs/2607.27432
AB - We propose dynamical low-rank (DLRA) filters for data-assimilation problems based on stochastic differential equations (SDEs). We first consider a Kalman filter applied to a Euler-Maruyama discretization of the SDE and observation processes, and derive a DLRA Kalman-type filter, named DLRA-JMCO, by minimizing jointly the error on the mean and covariance. We then obtain a time continuous DLRA-JMCO filter as the continuous limit of the time discrete one, and introduce a corresponding particle approximation. We also propose a strategy to enrich the DLRA-JMCO filter with a simple Gaussian process to capture the neglected dynamics in the orthogonal to the DLRA subspace. This correcting term allows the DLRA subspace evolution to be directly influenced by the observation operator. We finally propose a particle filter version of the DLRA-JMCO filter. Numerical experiments assess the performance of the proposed filters.
ER -