Work

Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients

Year: 2026

Type: preprint

Abstract: 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 model that projects the equations on a time-varying low dimensional subspace following the evolution of the solution. Well posedness results for the resulting DLRA equations have been proved in arXiv:2308.11581 under the assumption of global Lipschitz continuity and linear growth of the drift and the diffusion coefficients. In this work, we extend the existence result to the case of locally Lipschitz coefficient and we prove uniqueness of solutions under the assumption of a mild growth of the Lipschitz constant to infinity.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20307

Authors: Kazashi, Yoshihito, Nobile, Fabio, Zoccolan, Fabio

Institutions: University of Manchester, École Polytechnique Fédérale de Lausanne

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Award: Dynamical low rank methods for uncertainty quantification and data assimilation

OpenAlex ID: W7172104656

Cites: 4

Cited by:

Related to: 10