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l1-based calibration of POD-Galerkin models of two-dimensional unsteady flows

l1-based calibration of POD-Galerkin models of two-dimensional unsteady flows
l1-based calibration of POD-Galerkin models of two-dimensional unsteady flows
This paper discusses a physics–informed methodology aimed at reconstructing efficiently the fluid state of a system. Herein, the generation of an accurate reduced order model of two-dimensional unsteady flows from data leverages on sparsity-promoting statistical learning techniques. The cornerstone of the approach is l1 regularised regression, resulting in sparsely-connected models where only the important quadratic interactions between modes are retained. The original dynamical behaviour is reproduced at low computational costs, as few quadratic interactions need to be evaluated. The approach has two key features. First, interactions are selected systematically as a solution of a convex optimisation problem and no a priori assumptions on the physics of the flow are required. Second, the presence of a regularisation term improves the predictive performance of the original model, generally affected by noise and poor data quality. Test cases are for two-dimensional lid-driven cavity flows, at three values of the Reynolds number for which the motion is chaotic and energy interactions are scattered across the spectrum. It is found that: a) the sparsification generates models maintaining the original accuracy level but with a lower number of active coefficients; this becomes more pronounced for increasing Reynolds numbers suggesting that extension of these techniques to real-life flow configurations is possible; b) sparse models maintain a good temporal stability for predictions. The methodology is ready for more complex applications without modificationsof the underlying theory, and the integration into a cyber–physical model is feasible.
Cavity flow, l1 regularization, reduced complexity model
1000-9361
226-236
Rubini, Riccardo
f4c1935d-8a1a-4bec-b01a-01ddaf9a62ee
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Da Ronch, Andrea
a2f36b97-b881-44e9-8a78-dd76fdf82f1a
Rubini, Riccardo
f4c1935d-8a1a-4bec-b01a-01ddaf9a62ee
Lasagna, Davide
0340a87f-f323-40fb-be9f-6de101486b24
Da Ronch, Andrea
a2f36b97-b881-44e9-8a78-dd76fdf82f1a

Rubini, Riccardo, Lasagna, Davide and Da Ronch, Andrea (2021) l1-based calibration of POD-Galerkin models of two-dimensional unsteady flows. Chinese Journal of Aeronautics, 34 (1), 226-236. (doi:10.1016/j.cja.2020.10.009).

Record type: Article

Abstract

This paper discusses a physics–informed methodology aimed at reconstructing efficiently the fluid state of a system. Herein, the generation of an accurate reduced order model of two-dimensional unsteady flows from data leverages on sparsity-promoting statistical learning techniques. The cornerstone of the approach is l1 regularised regression, resulting in sparsely-connected models where only the important quadratic interactions between modes are retained. The original dynamical behaviour is reproduced at low computational costs, as few quadratic interactions need to be evaluated. The approach has two key features. First, interactions are selected systematically as a solution of a convex optimisation problem and no a priori assumptions on the physics of the flow are required. Second, the presence of a regularisation term improves the predictive performance of the original model, generally affected by noise and poor data quality. Test cases are for two-dimensional lid-driven cavity flows, at three values of the Reynolds number for which the motion is chaotic and energy interactions are scattered across the spectrum. It is found that: a) the sparsification generates models maintaining the original accuracy level but with a lower number of active coefficients; this becomes more pronounced for increasing Reynolds numbers suggesting that extension of these techniques to real-life flow configurations is possible; b) sparse models maintain a good temporal stability for predictions. The methodology is ready for more complex applications without modificationsof the underlying theory, and the integration into a cyber–physical model is feasible.

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l1-based calibration of POD Galerkin models - Accepted Manuscript
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Accepted/In Press date: 20 August 2020
e-pub ahead of print date: 7 November 2020
Published date: January 2021
Additional Information: Publisher Copyright: © 2020
Keywords: Cavity flow, l1 regularization, reduced complexity model

Identifiers

Local EPrints ID: 443365
URI: http://eprints.soton.ac.uk/id/eprint/443365
ISSN: 1000-9361
PURE UUID: a2623230-80b1-4aab-88d4-d021677480c0
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

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Date deposited: 21 Aug 2020 16:31
Last modified: 17 Mar 2024 05:51

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Contributors

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

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