Spatio-temporal data reconstruction analysis via kernel-based proper orthogonal decomposition

Autor(es)

Marcondes, Rebeca ; Ricciardi, Tulio ; Wolf, William

• Tipo de documento: Artigo Científico
• Fonte: AIAA SCITECH 2021 FORUM; v. N/A, p. 15-pg., 2021-01-01.

Resumo

Proper orthogonal decomposition, POD, has been widely used in the community of fluid dynamics. 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 into 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. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 13/08293-7 - CECC - Centro de Engenharia e Ciências Computacionais
• Beneficiário: Munir Salomao Skaf
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs