Fluid Flow Prediction in Porous Media using Sparse Data and Physics-Informed PointNet*

For the first time, we predict Stokes flow on pore scale in porous media by integrating sparse scattered labeled data and physics-informed PointNet (PIPN). PIPN is categorized as weakly-supervised deep learning such that its loss function is constructed by residuals of the continuity and linear momentum equations of incompressible flows and the mismatch between the neural network predictions and sparse observations. Compared to regular physics-informed neural networks, PIPN converges with lower resolutions of inquiry points, saving computational costs. PIPN has advantages over physics-informed convolutional neural networks in case of porous media. First, the PIPN input is exclusively the pore space (rather than both the grain and pore spaces), requiring less GPU memory. Second, density of inquiry point distribution can freely vary over the pore space in PIPN, allowing users to represent the pore space geometry and its boundaries smoothly and realistically. Third, PIPN can be conveniently integrated with spatially-unstructured data without any data interpolation. We examine the performance of the proposed PIPN framework by prediction of the velocity fields and consequently permeability of digital rocks with different spatial correlation lengths and porosities.