English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this work we demonstrate that SVD-based model reduction techniques knownfor ordinary differential equations, such as the proper orthogonaldecomposition, can be extended to stochastic differential equations in order toreduce the computational cost arising from both the high dimension of theconsidered stochastic system and the large number of independent Monte Carloruns. We also extend the proper symplectic decomposition method to stochasticHamiltonian systems, both with and without external forcing, and argue thatpreserving the underlying symplectic or variational structures results in moreaccurate and stable solutions that conserve energy better than when thenon-geometric approach is used. We validate our proposed techniques withnumerical experiments for a semi-discretization of the stochastic nonlinearSchr\"odinger equation and the Kubo oscillator.

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