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

TL;DR

This work tackles predicting time-dependent breakthrough curves $a(t)$ from 3D pore-scale geometry under fixed $(\mathrm{Pe}_L,\mathrm{Da}_L)=(5,0.1)$, using scarce data to motivate efficient surrogate modeling. It develops greedy kernel approaches (VKOGA) with data-adapted two-layer kernels to map high-dimensional voxel geometries to breakthrough curves, employing both morphology-based features and PCA-derived features. The results show that two-layer kernels yield high-accuracy predictions, with PCA-based features approaching the performance of morphology-based features, even in a data-scarce regime, and with substantial reductions in computation relative to full-order simulations. These findings support fast, accurate surrogate modeling for design and optimization tasks in porous media flows, and point to future integrations with CNNs and data augmentation strategies.

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.

Figures (7)

• Figure 1: Isometric (left) and middle plane (right) view of a typical porous sample; colors: brown - washcoat ($\Omega_w$), grey - solid (binder, $\Omega_s$), white (transparent) - free pores ($\Omega_f$), green - inlet boundary section, opposite of the (non-visible) - outlet section. GeoDict visualization Geodict2022.
• Figure 2: Two feature extraction strategies based models to approximate breakthrough curves from voxel data: Model with morphological features (MF), and model with PCA features (PCA).
• Figure 3: All breakthrough curves $a_i(t)$ computed from the voxel data $\mathbf{z}_i$ for $i\in \{1, \dots, 59 \}$.
• Figure 4: MF-1L-kernel: Predicted breakthrough curves on the test set $X_{\mathrm{test}}$ for three different training--test splits. Solid: Breaktrough curves, dotted: predictions. The different colours correspond to the different breakthrough curves.
• Figure 5: MF-2L-kernel: Predicted breakthrough curves on the test set $X_{\mathrm{test}}$ for three different training--test splits. Solid: Breaktrough curves, dotted: predictions. The different colours correspond to the different breakthrough curves.