  We show that the permeability of 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 simulations of flow through periodic
unit cells containing complex shaped obstacles. The prediction is achieved by
training a deep neural network (DNN) 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 determine the
permeability, although the functional relation between the MTs and the
permeability could be complex to determine.
