We show that the permeability of periodic simply connected porous media can be reliably predicted from the Minkowski tensors (MTs) describing the pore microstructure geometry. To this end, we consider a large number of two-dimensional simulations of flow through periodic unit cells containing complex-shaped obstacles. The prediction is achieved by training a deep neural network using the simulation data with the MT elements as attributes. The obtained predictions allow for the conclusion that MTs of the pore microstructure contain sufficient information to characterize the permeability, although the functional relation between the MTs and the permeability could be complex to determine.

中文翻译：

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简单连接的多孔微结构的Minkowski张量可以表征其渗透率吗？

我们表明，可以通过描述孔微结构几何形状的Minkowski张量（MTs）可靠地预测周期性简单连接的多孔介质的渗透率。为此，我们考虑了对包含复杂形状障碍物的周期性晶胞进行大量二维流动模拟。通过使用MT元素作为属性的模拟数据训练深度神经网络来实现预测。获得的预测可以得出这样的结论，即孔隙微结构的MTs包含足够的信息来表征渗透率，尽管要确定MTs和渗透率之间的功能关系很复杂。