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

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Title: Non-intrusive reduced order modelling with least squares fitting on a sparse grid
Authors: Lin, Z
Xiao, D
Fang, F
Pain, CC
Navon, I
Item Type: Journal Article
Abstract: This article presents a non-intrusive reduced order model (NIROM) 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 is required by this methodology and the level of non-intrusiveness is improved compared to existing ROMs. 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 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.
Issue Date: 8-Jul-2016
Date of Acceptance: 1-Jun-2016
URI: http://hdl.handle.net/10044/1/34448
DOI: htpps://dx.doi.org/10.1002/fld.4268
ISSN: 0271-2091
Publisher: Wiley
Start Page: 291
End Page: 306
Journal / Book Title: International Journal for Numerical Methods in Fluids
Volume: 83
Issue: 3
Copyright Statement: © 2016 John Wiley & Sons, Ltd. This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/fld.4268
Sponsor/Funder: Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Funder's Grant Number: NE/J015938/1
EP/K003976/1
RG80519
Keywords: Science & Technology
Technology
Physical Sciences
Computer Science, Interdisciplinary Applications
Mathematics, Interdisciplinary Applications
Mechanics
Physics, Fluids & Plasmas
Computer Science
Mathematics
Physics
non-intrusive
least squares fitting
POD
Smolyak sparse grid
PROPER ORTHOGONAL DECOMPOSITION
NAVIER-STOKES EQUATIONS
SHALLOW-WATER EQUATIONS
VARIATIONAL DATA ASSIMILATION
PETROV-GALERKIN METHODS
EMPIRICAL INTERPOLATION
NONLINEAR MODEL
REDUCTION
STRATEGIES
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Applied Mathematics
Publication Status: Published
Appears in Collections:Faculty of Engineering
Earth Science and Engineering



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