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ENCIT 2020
18th Brazilian Congress of Thermal Sciences and Engineering
Reconstruction of spatio-temporal flow datasets via kernel-based non-linear proper orthogonal decomposition
Submission Author:
Rebeca Marcondes , SP
Co-Authors:
Rebeca Marcondes, Tulio Rodarte Ricciardi, William Wolf
Presenter: Rebeca Marcondes
doi://10.26678/ABCM.ENCIT2020.CIT20-0172
Abstract
Proper orthogonal decomposition, POD, has been widely used in the community of fluid dynamics. The POD finds application in analysis of coherent flow structures, data compression and construction of reduced-order models, ROMs. However, in the latter case, ROMs are typically unstable for problems that present strong non-linearities, such as shock waves and contact surfaces, or a broad range of temporal and spatial scales, in turbulent flows. The kernel proper orthogonal decomposition KPOD is a promising method for overcoming the previous issues since it maps the non-linear data into a higher dimension, known as feature space, using kernel functions. One expects that non-linear features are incorporated in the KPOD basis such that fewer modes are required for a better approximation of the data. In this work, we employ both the POD and KPOD for the reconstruction of non-linear solutions from a modified Shu-Osher shock tube problem and the Ginzburg-Landau equation. A Radial Basis Function Neural Network is applied for the reconstructions and results show that the KPOD is a promising technique compared to the standard POD.
Keywords
Proper orthogonal decomposition (POD), Principal component analysis (PCA), kernel methods, dataset reconstruction, neural networks
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