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/ | ||||||||
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Document Type: | Article | ||||||||
Title: | Gradient-enhanced surrogate modeling based on proper orthogonal decomposition | ||||||||
Authors: |
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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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