Prediction of Steady-State Flow through Porous Media Using Machine Learning Models

2026-03-06

AI Summary

This study addresses the high computational cost of traditional computational fluid dynamics (CFD) in simulating steady-state flow through complex porous media, which hinders applications such as topology optimization. To overcome this limitation, the authors develop a machine learning–based surrogate model to predict solutions of the Navier-Stokes-Brinkman equations. They systematically compare convolutional autoencoders, U-Net, and the Fourier Neural Operator (FNO), incorporating a physics-informed loss function to enhance physical consistency. This work presents the first comprehensive evaluation of FNO for this task, demonstrating its mesh-invariant properties and suitability for topology optimization. Experimental results show that FNO achieves the lowest mean squared error (0.0017) and accelerates inference by up to 1,000× compared to conventional CFD, significantly outperforming baseline methods in both accuracy and generalization capability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively expensive for large and complex geometries. In contrast, data-driven surrogate models provide a computationally efficient alternative, enabling rapid and reliable predictions. In this study, we develop a machine-learning framework for predicting steady-state flow through porous media governed by the Navier-Stokes-Brinkman equations. We implement and compare three model architectures-convolutional autoencoder (AE), U-Net, and Fourier Neural Operator (FNO)-evaluating their predictive performance. To enhance physics consistency, we incorporate physics-informed loss functions. Our results demonstrate that FNO outperforms AE and U-Net, achieving a mean squared error (MSE) as low as 0.0017 while providing speedups of up to 1000 times compared to CFD. Additionally, the mesh-invariant property of FNO emphasizes its suitability for topology optimisation tasks, where varying mesh resolutions are required. This study highlights the potential of machine learning to accelerate fluid flow predictions in porous media, offering a scalable alternative to traditional numerical methods.

Problem

• porous media
• steady-state flow
• computational fluid dynamics
• topology optimisation
• machine learning

Innovation

• Fourier Neural Operator
• physics-informed machine learning
• porous media flow
• topology optimisation
• surrogate modeling