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

2026-05-22 · Source: cs.LG updates on arXiv.org · Field: Science & Research — Engineering & Applied Sciences, Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

A neural-network-based framework for predicting pore-scale velocity fields in porous media is presented, utilizing a convolutional encoder-decoder (U-Net) architecture with skip connections. The method incorporates a custom loss function that enforces physical consistency, including terms for incompressibility, no-flow conditions within solids, periodicity constraints, and agreement with the global tortuosity index. The ResNet-101 architecture demonstrated superior performance, achieving a velocity RMSE of 5.1e-03 and a tortuosity R^2 of 0.983. The model exhibits strong generalization capabilities across variations in obstacle geometry, boundary conditions (e.g., pipe-like flows), and porosities within the training range of 0.70 to 0.95, and even to real Li-O2 electrode microstructures. Furthermore, using the network's predictions to initialize Lattice-Boltzmann Method (LBM) simulations significantly accelerated convergence in over 90% of cases, reducing iterations by a median of 50%. Inference time is 5 ms on GPU, substantially faster than LBM's 560 ms on CPU.

Key takeaway

For fluid dynamics researchers or engineers simulating porous media flow, you should consider integrating physics-informed convolutional neural networks. This approach significantly accelerates Lattice-Boltzmann Method (LBM) simulations by providing warm starts, reducing convergence time by a median of 50% in over 90% of cases. You can achieve high accuracy in pore-scale velocity predictions and macroscopic properties like tortuosity and permeability, even for out-of-distribution geometries, using a ResNet-101 backbone and a custom multi-term loss function.

Key insights

Physics-informed CNNs accurately predict fluid flow in porous media, significantly accelerating traditional LBM simulations.

Principles

• Custom loss functions enhance physical consistency in neural network predictions.
• Architectural complexity doesn't always improve accuracy for fixed-grid flow mapping.
• Generalization to out-of-distribution data is possible with physics-informed training.

Method

A U-Net encoder-decoder with skip connections predicts pore-scale velocity from binary geometry. A custom loss function combines velocity MSE with penalties for incompressibility, no-flow in solids, periodicity, and tortuosity matching.

In practice

• Initialize LBM simulations with CNN predictions for 50% faster convergence.
• Apply physics-informed loss to improve model generalization for fluid dynamics.
• Use ResNet-101 for high accuracy in pore-scale velocity field prediction.

Topics

• Physics-informed Neural Networks
• Pore-scale Fluid Flow
• Porous Media Simulation
• Lattice Boltzmann Method
• U-Net Architecture
• Model Generalization

Code references

• dioscuri-tda/PhysInfPorousFluidFlow

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

Related on AIssential

• A Validated LBM Dataset and Pipeline for Surrogate Modeling of Turbulent 3D Obstructed Channel Flows — A validated LBM dataset and pipeline enable standardized evaluation of neural operators for 3D turbulent flows.
• Differential Equations V — Physics Informed Neural Networks (PINNs) — Physics Informed Neural Networks embed physical laws into neural networks for fast, accurate, and physically consistent simulations.
• Physics-Guided Spatiotemporal Learning for Coastal Wave Peak Period Estimation from Video — Physics-guided deep spatiotemporal learning from video can accurately and consistently estimate coastal wave peak periods, overcoming traditional monitoring limitations.
• The Physics Bug That Stumped Everyone Is Finally Gone! — A physics-based simulation technique achieves highly accurate and efficient fluid-solid interactions through two-way coupling.
• Droplet-LNO: Physics-Informed Laplace Neural Operators for Accurate Prediction of Droplet Spreading Dynamics on Complex Surfaces — PI-LNO uses Laplace transforms and physics-informed neural networks to model droplet spreading dynamics efficiently.
• Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport — SciML, combining reduced-order models and neural networks with HPC, efficiently approximates complex coupled fluid flow and transport, significantly cutting computational costs.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.