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.

翻译：求解多孔介质流动是现代热管理关键部件——冷板拓扑优化中的关键步骤。传统的计算流体动力学（CFD）方法虽然精确，但对于大型复杂几何结构往往计算成本过高。相比之下，数据驱动的代理模型提供了一种计算高效的替代方案，能够实现快速可靠的预测。本研究开发了一个机器学习框架，用于预测由Navier-Stokes-Brinkman方程控制的多孔介质稳态流动。我们实现并比较了三种模型架构——卷积自编码器（AE）、U-Net和傅里叶神经算子（FNO），评估了它们的预测性能。为提高物理一致性，我们引入了物理信息损失函数。结果表明，FNO的表现优于AE和U-Net，其均方误差（MSE）可低至0.0017，同时相比CFD实现了高达1000倍的加速。此外，FNO的网格无关特性凸显了其在拓扑优化任务中的适用性，因为此类任务需要不同的网格分辨率。本研究凸显了机器学习在加速多孔介质流体流动预测方面的潜力，为传统数值方法提供了一种可扩展的替代方案。