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

TL;DR

This paper introduces a greedy kernel approximation method to efficiently predict breakthrough curves in 3D porous reactive flow simulations, addressing the challenge of scarce data and high-dimensional inputs.

Contribution

It demonstrates the effectiveness of vectorial kernel orthogonal greedy approximation with a data-adapted kernel for high-dimensional, scarce data reactive flow prediction.

Findings

VKOGA yields high accuracy in predicting breakthrough curves.

Kernel methods outperform standard machine learning in scarce data scenarios.

Efficient meshless approximation for complex 3D flow data.

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 available few data samples, while the input and output dimensions are high. In this scarce data setting, standard machine learning methods are likely to ail. 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.