Can Minkowski tensors of a simply connected porous microstructure characterize its permeability

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.