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We predict steady-state Stokes flow of fluids within porous media at porescales using sparse point observations and a novel class of physics-informedneural networks, called "physics-informed PointNet" (PIPN). Taking theadvantages of PIPN into account, three new features become available comparedto physics-informed convolutional neural networks for porous mediumapplications. First, the input of PIPN is exclusively the pore spaces of porousmedia (rather than both the pore and grain spaces). This feature diminishesrequired computer memory. Second, PIPN represents the boundary of pore spacessmoothly and realistically (rather than pixel-wise representations). Third,spatial resolution can vary over the physical domain (rather than equallyspaced resolutions). This feature enables users to reach an optimal resolutionwith a minimum computational cost. The performance of our framework isevaluated by the study of the influence of noisy sensor data, pressureobservations, and spatial correlation length.

Prediction of fluid flow in porous media by sparse observations and physics-informed PointNet