  We propose a novel deep learning framework for predicting permeability of
porous media from their digital images. Unlike convolutional neural networks,
instead of feeding the whole image volume as inputs to the network, we model
the boundary between solid matrix and pore spaces as point clouds and feed them
as inputs to a neural network based on the PointNet architecture. This approach
overcomes the challenge of memory restriction of graphics processing units and
its consequences on the choice of batch size, and convergence. Compared to
convolutional neural networks, the proposed deep learning methodology provides
freedom to select larger batch sizes, due to reducing significantly the size of
network inputs. Specifically, we use the classification branch of PointNet and
adjust it for a regression task. As a test case, two and three dimensional
synthetic digital rock images are considered. We investigate the effect of
different components of our neural network on its performance. We compare our
deep learning strategy with a convolutional neural network from various
perspectives, specifically for maximum possible batch size. We inspect the
generalizability of our network by predicting the permeability of real-world
rock samples as well as synthetic digital rocks that are statistically
different from the samples used during training. The network predicts the
permeability of digital rocks a few thousand times faster than a Lattice
Boltzmann solver with a high level of prediction accuracy.
