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Gradient-enhanced surrogate modeling based on proper orthogonal decomposition

Zimmermann, Ralf (2013) Gradient-enhanced surrogate modeling based on proper orthogonal decomposition. Journal of Computational and Applied Mathematics, 237 (1), pp. 403-418. Elsevier. DOI: 10.1016/j.cam.2012.06.010

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Abstract

A new method for enhanced surrogate modeling of complex systems by exploiting gradient information is presented. The technique combines the proper orthogonal decomposition (POD) and interpolation methods capable of fitting both sampled input values and sampled derivative information like Kriging (aka spatial Gaussian processes). In contrast to existing POD-based interpolation approaches, the gradient-enhanced method takes both snapshots and partial derivatives of snapshots of the associated full-order model (FOM) as an input. It is proved that the resulting predictor reproduces these inputs exactly up to the standard POD truncation error. Hence, the enhanced predictor can be considered as (approximately) first-order accurate at the snapshot locations. The technique applies to all fields of application, where derivative information can be obtained efficiently, for example via solving associated primal or adjoint equations. This includes, but is not limited to Computational Fluid Dynamics (CFD). The method is demonstrated for an academic test case exhibiting the main features of reduced-order modeling of partial differential equations.

Item URL in elib:https://elib.dlr.de/77995/
Document Type:Article
Title:Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Zimmermann, RalfUNSPECIFIEDUNSPECIFIED
Date:1 January 2013
Journal or Publication Title:Journal of Computational and Applied Mathematics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:237
DOI :10.1016/j.cam.2012.06.010
Page Range:pp. 403-418
Publisher:Elsevier
Status:Published
Keywords:Proper Orthogonal Decomposition, Kriging, CFD
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research (old)
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation & Validation (old)
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Deposited By: Görtz, Stefan
Deposited On:10 Jan 2013 16:44
Last Modified:06 Sep 2019 15:19

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