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

TL;DR

This paper presents a machine learning framework using FNO to predict steady-state flow in porous media, significantly reducing computational costs and enabling efficient topology optimization.

Contribution

It introduces a physics-informed FNO model that outperforms other architectures in accuracy and speed, with mesh-invariance suitable for complex geometries.

Findings

FNO achieves MSE as low as 0.0017

Provides up to 1000x speedup over CFD methods

Mesh-invariance enhances topology optimization capabilities

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.