Greedy Kernel Methods for Approximating Breakthrough Curves for Reactive Flow from 3D Porous Geometry Data

Robin Herkert (), Patrick Buchfink, Tizian Wenzel, Bernard Haasdonk, Pavel Toktaliev and Oleg Iliev
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Robin Herkert: Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, 70569 Stuttgart, Germany
Patrick Buchfink: Department of Applied Mathematics, University of Twente, 7522 NH Enschede, The Netherlands
Tizian Wenzel: Department of Mathematics, Universität Hamburg, 20146 Hamburg, Germany
Bernard Haasdonk: Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, 70569 Stuttgart, Germany
Pavel Toktaliev: Fraunhofer ITWM, Technical University Kaiserslautern, 67663 Kaiserslautern, Germany
Oleg Iliev: Fraunhofer ITWM, Technical University Kaiserslautern, 67663 Kaiserslautern, Germany

Mathematics, 2024, vol. 12, issue 13, 1-17

Abstract: We address the challenging application of 3D pore scale reactive flow under varying geometry parameters. The task is to predict time-dependent integral quantities, i.e., breakthrough curves, from the given geometries. As the 3D reactive flow simulation is highly complex and computationally expensive, we are interested in data-based surrogates that can give a rapid prediction of the target quantities of interest. This setting is an example of an application with scarce data, i.e., only having a few available data samples, while the input and output dimensions are high. In this scarce data setting, standard machine learning methods are likely to fail. Therefore, we resort to greedy kernel approximation schemes that have shown to be efficient meshless approximation techniques for multivariate functions. We demonstrate that such methods can efficiently be used in the high-dimensional input/output case under scarce data. Especially, we show that the vectorial kernel orthogonal greedy approximation (VKOGA) procedure with a data-adapted two-layer kernel yields excellent predictors for learning from 3D geometry voxel data via both morphological descriptors or principal component analysis.

Keywords: machine learning; kernel methods; two-layered kernels; porous media; breakthrough curves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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