Work

Further Approaches of Dynamical Low-Rank Approximation for SDEs

Year: 2026

Type: preprint

Abstract: 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 functionals and (informally) from a Stratonovich formulation, respectively. The former approach resembles the DLRA for SDE system proposed in arXiv:1803.00499. Providing the differentiability of the diffusion, the latter procedure registers an additional term in the drift. Indeed, its derivation exploits the Stratonovich formulation to write stochastic processes on manifold, and, hence, possesses a term that depends on the geometry of the manifold itself. These developments open the debate on which formalism is more suitable and what DLRA for SDEs really is. MSC classes: 58J65, 60H10, 60H35, 65C30

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20292

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: W7172104408

Cites:

Cited by:

Related to: 10