Point-cloud neural network predicts porous media permeability

Convolutional neural network (CNN), a machine learning method that maps digital images based on layers of artificial neurons, is used extensively to predict the permeability of porous media, like rocks or ceramic. The challenge is the amount of graphics processing unit (GPU) memory required, as more filters are added to extract additional data from imagery.

Kashefi and Mukerji propose a point-cloud neural network that relaxes GPU memory restrictions in CNNs. They achieve this by modeling porous media representing the grain-pore space boundaries as point sets rather than images.

The point-cloud neural network is based on the PointNet architecture developed at Stanford University. PointNet represents 3D objects using a set of points in space, rather than using 2D images.

Compared to CNN, they found the point-cloud neural network consumes significantly less GPU memory, allowing larger batches, the amount of data a network processes in one iteration of the learning process.

“Mathematically, the permeability of a porous medium is a function of the velocity fields in the pore space, and the solution of the velocity field depends on the grain-pore boundary,” Ali Kashefi said. “Thus, if we represent the geometry of grain-pore boundaries as a set of points, then the volume of the grain or pore spaces is not needed.”

The approach may be used for other machine learning problems, where the output of interest is a real number that is a function of the spatial domain geometry. For example, a set of points representing the body surface of airfoils can be used to predict the associated lift and drag.

Source: “Point-cloud deep learning of porous media for permeability prediction,” by Ali Kashefi and Tapan Mukerji, Physics of Fluids (2021). The article can be accessed at https://doi.org/10.1063/5.0063904 .