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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper discusses a non-intrusive data-driven model order reduction methodthat learns low-dimensional dynamical models for a parametrized shallow waterequation. We consider the shallow water equation in non-traditional form(NTSWE). We focus on learning low-dimensional models in a non-intrusive way.That means, we assume not to have access to a discretized form of the NTSWE inany form. Instead, we have snapshots that are obtained using a black-boxsolver. Consequently, we aim at learning reduced-order models only from thesnapshots. Precisely, a reduced-order model is learnt by solving an appropriateleast-squares optimization problem in a low-dimensional subspace. Furthermore,we discuss computational challenges that particularly arise from theoptimization problem being ill-conditioned. Moreover, we extend thenon-intrusive model order reduction framework to a parametric case where wemake use of the parameter dependency at the level of the partial differentialequation. We illustrate the efficiency of the proposed non-intrusive method toconstruct reduced-order models for NTSWE and compare it with an intrusivemethod (proper orthogonal decomposition). We furthermore discuss the predictivecapabilities of both models outside the range of the training data.

Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation