6 papers
Numerical Methods for Dynamical Low-Rank Approximations of Stochastic Differential Equations -- Part II: Stochastic discretization
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
This paper is the follow up (Part II) of arXiv:2601.21428, which proposed and analyzed time discretization schemes for the Dynamical Low-Rank Approximation (DLRA) of high-dimension…
Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this work, we consider the Dynamical Low Rank Approximation (DLRA) of a high-dimensional system of Stochastic Differential Equations (SDEs); DLRA is an effective reduced order m…
Further Approaches of Dynamical Low-Rank Approximation for SDEs
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this article, we propose two other DLRA-type dynamics for stochastic differential equations (SDEs) than the one studied in arXiv:2308.11581, derived from a minimization of funct…
Dynamical Low-Rank Smoothing
Youssef Marzouk, Fabio Nobile, Fabio Zoccolan
Computational costs often make smoothing procedures prohibitive for high-dimensional data assimilation problems. To address this challenge, we propose a dynamical low-rank approxim…
Dynamical Low-Rank Filters for Data Assimilation
Yoshihito Kazashi, Youssef Marzouk, Fabio Nobile +1
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-…
Numerical Methods for Dynamical Low-Rank Approximations of Stochastic Differential Equations -- Part I: Time discretization
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this work (Part I), we study three time-discretization schemes for the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Spec…