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PCAfold: Python software to generate, analyze and improve PCA-derived low-dimensional manifolds

par Zdybal, Kamila ;Armstrong, Elizabeth;Parente, Alessandro ;Sutherland, James
Référence Combura Symposium 2021 (2021-11-10: Soesterberg, the Netherlands)
Publication Publié, 2021-10-29

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Résumé :

Many research disciplines exhibit growing interest in low-dimensional data representations. Parameterizing high-dimensional data sets with fewer variables allows for an easier treatment and handling of multivariate data sets. In addition, reduced-order models (ROMs) can be built in lower-dimensional spaces. ROM is particularly appealing for combustion modeling. Combustion couples the complexity of fluid flow and chemical reactions, making simulations computationally challenging. In recent years, Principal Component Analysis (PCA) became an established dimensionality reduction technique in combustion modeling. In this work, we describe PCAfold, a Python software package that allows to generate low-dimensional manifolds by projecting the original data set onto a lower-dimensional PCA-basis. PCAfold exploits the idea that the parameterization obtained via dimensionality reduction is not unique. It can be altered through data preprocessing including scaling, sampling or subsetting. Once the manifold is obtained, novel functionalities are implemented in PCAfold that allow to assess the quality of manifold topologies. Two important features of a well-defined manifold include uniqueness and moderate gradients in the dependent variable space.