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Non-intrusive reduced order modelling with least squares fitting on a sparse grid

Z. Lin, D. Xiao, F. Fang, C. C. Pain, Ionel M. Navon, Dunhui Xiao Orcid Logo

International Journal for Numerical Methods in Fluids, Volume: 83, Issue: 3, Pages: 291 - 306

Swansea University Author: Dunhui Xiao Orcid Logo

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DOI (Published version): 10.1002/fld.4268

Abstract

This paper presents a non‐intrusive reduced order model for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. The...

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Published in: International Journal for Numerical Methods in Fluids
ISSN: 0271-2091
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa46453
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spelling 2022-09-27T17:04:55.7782388 v2 46453 2018-12-06 Non-intrusive reduced order modelling with least squares fitting on a sparse grid 62c69b98cbcdc9142622d4f398fdab97 0000-0003-2461-523X Dunhui Xiao Dunhui Xiao true false 2018-12-06 AERO This paper presents a non‐intrusive reduced order model for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. Then we introduce a new least squares fitting procedure to approximate the dynamical transition of the POD coefficients between subsequent time steps, taking only a set of full model solution snapshots as the training data during the construction. Thus, neither the physical details nor further numerical simulations of the original PDE model are required by this methodology, and the level of non‐intrusiveness is improved compared with existing reduced order models. Furthermore, we take adaptive measures to address the instability issue arising from reduced order iterations of the POD coefficients. This model can be applied to a wide range of physical and engineering scenarios, and we test it on a couple of problems in fluid dynamics. It is demonstrated that this reduced order approach captures the dominant features of the high‐fidelity models with reasonable accuracy while the computation complexity is reduced by several orders of magnitude. Journal Article International Journal for Numerical Methods in Fluids 83 3 291 306 0271-2091 30 1 2017 2017-01-30 10.1002/fld.4268 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2022-09-27T17:04:55.7782388 2018-12-06T14:52:10.3619243 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Z. Lin 1 D. Xiao 2 F. Fang 3 C. C. Pain 4 Ionel M. Navon 5 Dunhui Xiao 0000-0003-2461-523X 6 0046453-13122018164120.pdf submissionv2.pdf 2018-12-13T16:41:20.2800000 Output 2397402 application/pdf Accepted Manuscript true 2018-12-13T00:00:00.0000000 true eng
title Non-intrusive reduced order modelling with least squares fitting on a sparse grid
spellingShingle Non-intrusive reduced order modelling with least squares fitting on a sparse grid
Dunhui Xiao
title_short Non-intrusive reduced order modelling with least squares fitting on a sparse grid
title_full Non-intrusive reduced order modelling with least squares fitting on a sparse grid
title_fullStr Non-intrusive reduced order modelling with least squares fitting on a sparse grid
title_full_unstemmed Non-intrusive reduced order modelling with least squares fitting on a sparse grid
title_sort Non-intrusive reduced order modelling with least squares fitting on a sparse grid
author_id_str_mv 62c69b98cbcdc9142622d4f398fdab97
author_id_fullname_str_mv 62c69b98cbcdc9142622d4f398fdab97_***_Dunhui Xiao
author Dunhui Xiao
author2 Z. Lin
D. Xiao
F. Fang
C. C. Pain
Ionel M. Navon
Dunhui Xiao
format Journal article
container_title International Journal for Numerical Methods in Fluids
container_volume 83
container_issue 3
container_start_page 291
publishDate 2017
institution Swansea University
issn 0271-2091
doi_str_mv 10.1002/fld.4268
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
document_store_str 1
active_str 0
description This paper presents a non‐intrusive reduced order model for general, dynamic partial differential equations. Based upon proper orthogonal decomposition (POD) and Smolyak sparse grid collocation, the method first projects the unknowns with full space and time coordinates onto a reduced POD basis. Then we introduce a new least squares fitting procedure to approximate the dynamical transition of the POD coefficients between subsequent time steps, taking only a set of full model solution snapshots as the training data during the construction. Thus, neither the physical details nor further numerical simulations of the original PDE model are required by this methodology, and the level of non‐intrusiveness is improved compared with existing reduced order models. Furthermore, we take adaptive measures to address the instability issue arising from reduced order iterations of the POD coefficients. This model can be applied to a wide range of physical and engineering scenarios, and we test it on a couple of problems in fluid dynamics. It is demonstrated that this reduced order approach captures the dominant features of the high‐fidelity models with reasonable accuracy while the computation complexity is reduced by several orders of magnitude.
published_date 2017-01-30T03:58:02Z
_version_ 1763752943134179328
score 11.036706

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