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

TL;DR

This paper introduces a physics-informed convolutional neural network framework that accurately predicts fluid velocity fields in porous media, improving simulation efficiency and enabling faster convergence in computational fluid dynamics models.

Contribution

The authors develop a novel CNN architecture with a custom loss function incorporating physical constraints, demonstrating improved accuracy and generalization for pore-scale fluid flow prediction.

Findings

The model achieves accurate velocity predictions across diverse porous structures.

Incorporating physical constraints improves prediction accuracy and robustness.

Using predicted fields as initial conditions accelerates Lattice-Boltzmann simulations, reducing iterations by over 90%.

Abstract

Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly in intricate porous domains. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method uses a convolutional encoder-decoder architecture with skip connections to preserve spatial detail while extracting multi-scale features. Physical consistency is encouraged through a custom loss function combining velocity reconstruction with incompressibility, no-flow conditions inside solids, periodicity constraints, and agreement with the global tortuosity index. We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy. Several CNN backbones are evaluated to identify architectures providing accurate and robust predictions. The generalization ability of the trained model is tested on samples outside the training distribution, including changes in obstacle geometry, boundary conditions, porosity, and realistic porous structures. Finally, we demonstrate a practical use of the predicted velocity fields as initial conditions for Lattice-Boltzmann simulations. This warm-start strategy accelerates solver convergence, reducing the number of iterations in over 90% of tested cases.