In this work, the development of a framework for the multi-scale data-driven parametrization of averaged-scale models is outlined and applied to dispersive transport. Dispersive transport is a common phenomena included in transport models at the averaged scale, describing the velocity and geometry dependent mixing seen at the pore scale. Optimal parameters for the development of dispersion tensors can be extracted from pore-scale simulations in the form of an averaged velocity and characteristic length scales. In this work, the determination of these parameters is outlined and tested first on simple and later on complex random pore geometries. These parametrizations are then used to develop a data-driven model extracting optimal parameters from pore geometries. In order to better understand the relationships between these parameters and pore geometries, we introduce a series of metrics based on interfacial geometry, volume ratios, and connectivity. These metrics are then compared against the parametrizations, and used to develop a metrics based data-driven model.

翻译：本文概述了平均尺度模型的多尺度数据驱动参数化框架的构建，并将其应用于弥散输运问题。弥散输运是平均尺度输运模型中常见的现象，描述了在孔隙尺度上观测到的依赖于速度和几何结构的混合过程。发展弥散张量的最优参数可从孔隙尺度模拟中获取，其形式为平均速度和特征尺度长度。本文详细阐述并测试了这些参数的确定方法，首先在简单随机孔隙几何结构上验证，随后推广至复杂几何结构。基于这些参数化方案，我们构建了从孔隙几何结构中提取最优参数的数据驱动模型。为深入理解这些参数与孔隙几何结构之间的关联，我们引入了一系列基于界面几何特征、体积比及连通性的度量指标。通过对比度量指标与参数化结果，最终建立了基于度量的数据驱动模型。