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Adaptive sampling for nonlinear dimensionality reduction based on manifold learning

Franz, Thomas and Zimmermann, Ralf and Görtz, Stefan (2017) Adaptive sampling for nonlinear dimensionality reduction based on manifold learning. In: Model Reduction of Parametrized Systems Springer. pp. 255-269. ISBN 978-3-319-58785-1.

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We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime.

Item URL in elib:https://elib.dlr.de/114680/
Document Type:Book Section
Title:Adaptive sampling for nonlinear dimensionality reduction based on manifold learning
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Franz, ThomasThomas.Franz (at) dlr.deUNSPECIFIED
Zimmermann, Ralfzimmermann (at) imada.sdu.dkUNSPECIFIED
Görtz, StefanStefan.Goertz (at) dlr.deUNSPECIFIED
Journal or Publication Title:Model Reduction of Parametrized Systems
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Page Range:pp. 255-269
Keywords:Adaptive Sampling, Reduced Order Models, Manifold Learning, Isomap
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation
Location: Braunschweig
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > CASE, BS
Deposited By: Franz, Thomas
Deposited On:21 Nov 2017 11:25
Last Modified:21 Nov 2017 11:25

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