Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

Tomasz Tyranowski*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the computational cost arising from both the high dimension of the considered stochastic system and the large number of independent Monte Carlo runs. We also extend the proper symplectic decomposition method to stochastic Hamiltonian systems, both with and without external forcing, and argue that preserving the underlying symplectic or variational structures results in more accurate and stable solutions that conserve energy better than when the non-geometric approach is used. We validate our proposed techniques with numerical experiments for a semi-discretization of the stochastic nonlinear Schrödinger equation and the Kubo oscillator.
Original languageEnglish
Pages (from-to)220-255
Number of pages36
JournalJournal of Computational Dynamics
Volume11
Issue number2
Early online dateFeb 2024
DOIs
Publication statusPublished - Apr 2024

Keywords

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