  We predict steady-state Stokes flow of fluids within porous media at pore
scales using sparse point observations and a novel class of physics-informed
neural networks, called "physics-informed PointNet" (PIPN). Taking the
advantages of PIPN into account, three new features become available compared
to physics-informed convolutional neural networks for porous medium
applications. First, the input of PIPN is exclusively the pore spaces of porous
media (rather than both the pore and grain spaces). This feature diminishes
required computer memory. Second, PIPN represents the boundary of pore spaces
smoothly and realistically (rather than pixel-wise representations). Third,
spatial resolution can vary over the physical domain (rather than equally
spaced resolutions). This feature enables users to reach an optimal resolution
with a minimum computational cost. The performance of our framework is
evaluated by the study of the influence of noisy sensor data, pressure
observations, and spatial correlation length.
