The University of Southampton
University of Southampton Institutional Repository

A priori sparsification of Galerkin models

A priori sparsification of Galerkin models
A priori sparsification of Galerkin models

A methodology to generate sparse Galerkin models of chaotic/unsteady fluid flows containing a minimal number of active triadic interactions is proposed. The key idea is to find an appropriate set of basis functions for the projection representing elementary flow structures that interact minimally one with the other, resulting in a triadic interaction coefficient tensor with sparse structure. Interpretable and computationally efficient Galerkin models are obtained, since a reduced number of triadic interactions are computed to evaluate the right-hand side of the model. To find the basis functions, a subspace rotation technique is used, whereby a set of proper orthogonal decomposition (POD) modes is rotated into a POD subspace of larger dimension using coordinates associated with low-energy dissipative scales to alter energy paths and the structure of the triadic interaction coefficient tensor. This rotation is obtained as the solution of a non-convex optimisation problem that maximises the energy captured by the new basis, promotes sparsity and ensures long-term temporal stability of the sparse Galerkin system. We demonstrate the approach on two-dimensional lid-driven cavity flow at where the motion is chaotic and energy interactions are scattered in modal space. We show that the procedure generates Galerkin models with a reduced set of active triadic interactions, distributed in modal space according to established knowledge of scale interactions in two-dimensional flows. This property, however, is observed only if long-term temporal stability is included explicitly in the formulation, indicating that a dynamical constraint is necessary to obtain a physically consistent sparsification.

computational methods, low-dimensional models, machine learning
0022-1120
Rubini, Riccardo
f4c1935d-8a1a-4bec-b01a-01ddaf9a62ee
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Ronch, Andrea Da
a2f36b97-b881-44e9-8a78-dd76fdf82f1a
Rubini, Riccardo
f4c1935d-8a1a-4bec-b01a-01ddaf9a62ee
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Ronch, Andrea Da
a2f36b97-b881-44e9-8a78-dd76fdf82f1a

Rubini, Riccardo, Lasagna, Davide and Ronch, Andrea Da (2022) A priori sparsification of Galerkin models. Journal of Fluid Mechanics, 941, [A43]. (doi:10.1017/jfm.2022.318).

Record type: Article

Abstract

A methodology to generate sparse Galerkin models of chaotic/unsteady fluid flows containing a minimal number of active triadic interactions is proposed. The key idea is to find an appropriate set of basis functions for the projection representing elementary flow structures that interact minimally one with the other, resulting in a triadic interaction coefficient tensor with sparse structure. Interpretable and computationally efficient Galerkin models are obtained, since a reduced number of triadic interactions are computed to evaluate the right-hand side of the model. To find the basis functions, a subspace rotation technique is used, whereby a set of proper orthogonal decomposition (POD) modes is rotated into a POD subspace of larger dimension using coordinates associated with low-energy dissipative scales to alter energy paths and the structure of the triadic interaction coefficient tensor. This rotation is obtained as the solution of a non-convex optimisation problem that maximises the energy captured by the new basis, promotes sparsity and ensures long-term temporal stability of the sparse Galerkin system. We demonstrate the approach on two-dimensional lid-driven cavity flow at where the motion is chaotic and energy interactions are scattered in modal space. We show that the procedure generates Galerkin models with a reduced set of active triadic interactions, distributed in modal space according to established knowledge of scale interactions in two-dimensional flows. This property, however, is observed only if long-term temporal stability is included explicitly in the formulation, indicating that a dynamical constraint is necessary to obtain a physically consistent sparsification.

This record has no associated files available for download.

More information

e-pub ahead of print date: 4 May 2022
Published date: 25 June 2022
Additional Information: © The Author(s), 2022. Published by Cambridge University Press
Keywords: computational methods, low-dimensional models, machine learning

Identifiers

Local EPrints ID: 457833
URI: http://eprints.soton.ac.uk/id/eprint/457833
ISSN: 0022-1120
PURE UUID: 95cea309-ba82-453b-8eac-6b48b49f655a
ORCID for Davide Lasagna: ORCID iD orcid.org/0000-0002-6501-6041
ORCID for Andrea Da Ronch: ORCID iD orcid.org/0000-0001-7428-6935

Catalogue record

Date deposited: 20 Jun 2022 16:47
Last modified: 21 Jun 2022 01:42

Export record

Altmetrics

Contributors

Author: Riccardo Rubini
Author: Davide Lasagna ORCID iD
Author: Andrea Da Ronch ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×