用机器学习加速多孔介质流场预测，精度高且快千倍。
Prediction of Steady-State Flow through Porous Media Using Machine Learning Models
- 采用FNO等模型结合物理约束损失，提升预测准确性。
- FNO误差低至0.0017，计算速度比CFD快1000倍。
- 模型对网格不敏感，适合拓扑优化中的复杂结构设计。
多孔介质中的流动求解是现代热管理中冷板拓扑优化的关键步骤。传统计算流体动力学（CFD）方法虽准确，但对大规模复杂几何体计算成本过高。相比之下，数据驱动的代理模型可实现高效预测。本研究构建了基于机器学习的稳态流动预测框架，针对由纳维-斯托克斯-布林克曼方程控制的多孔介质流动，对比了卷积自编码器（AE）、U-Net和傅里叶神经算子（FNO）三种模型架构，并引入物理信息损失函数增强模型一致性。结果表明，FNO表现最优，均方误差（MSE）低至0.0017，相较CFD最高提速达1000倍。此外，FNO具备网格不变性，特别适用于需频繁调整网格分辨率的拓扑优化任务。该研究展示了机器学习在加速多孔介质流场预测方面的潜力，为传统数值方法提供了一种可扩展的替代方案。
原文摘要 · Abstract (English)
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.
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