Physics-informed convolutional neural networks for fluid flow through porous media.

Accurate simulation of fluid flow in porous media is a challenging task due to the complexity of pore-space geometries and the computational cost of solving the Navier-Stokes equations. Traditional numerical solvers rely on carefully constructed meshes, often requiring manual intervention, and typically exhibit slow convergence. This difficulty is particularly pronounced in porous media, where the diffusive nature of momentum transport is hindered by intricate solid boundaries. These challenges limit the efficiency of numerical simulations, particularly when repeated evaluations are required. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method is based on a convolutional encoder-decoder architecture with skip connections, designed to preserve fine-grained structural information. Physical consistency is encouraged through a custom loss function composed of multiple terms: incompressibility, no-flow conditions within solids, periodicity constraints, and agreement with the global tortuosity index. We systematically analyze the influence of weight selection for these loss terms, quantifying their individual contributions to prediction accuracy. Several architectural variants inspired by computer vision are evaluated to identify one providing the best performance and robustness. The generalization ability of the trained network is assessed on samples outside the training distribution, including variations in boundary conditions, obstacle geometry, and porosity. Finally, we demonstrate additional practical applications in which network predictions are used to initialize the Lattice-Boltzmann simulations, a standard fluid dynamics solver, often used in complex boundary problems like porous media and used by us to train the network. We have used network-generated velocity field as a starting point and found that this significantly accelerates LBM solver convergence, achieving improvements in over 90% of cases.