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.

翻译：本文研究了三维孔隙尺度反应流在不同几何参数下的挑战性应用。该任务旨在根据给定几何结构预测随时间变化的积分量，即穿透曲线。由于三维反应流模拟高度复杂且计算成本昂贵，我们关注能够快速预测目标感兴趣量的数据驱动代理模型。该场景是典型的小样本数据应用案例，即可用数据样本稀少，同时输入与输出维度较高。在此数据稀缺条件下，标准机器学习方法往往难以奏效。因此，我们采用贪婪核近似方案，该方案已被证明是多变量函数的高效无网格近似技术。我们证明此类方法能在数据稀缺的高维输入/输出场景中有效应用。特别地，我们通过形态描述符或主成分分析两种方式，展示了采用数据自适应双层核的向量核正交贪婪近似（VKOGA）方法，能够为三维几何体素数据学习构建卓越的预测模型。