用神经网络直接预测多孔介质中的流速场,提升模拟效率。
Physics-informed convolutional neural networks for fluid flow through porous media

- 基于卷积编码器-解码器结构,融合物理约束实现高精度流速预测。
- 预测结果在90%以上案例中显著减少格子玻尔兹曼模拟的迭代次数。
- 模型可泛化到不同孔隙结构、边界条件和真实多孔材料。
由于复杂的孔隙几何结构及求解纳维-斯托克斯方程的高计算成本,多孔介质中流体流动的精确模拟极具挑战性,尤其在需要重复模拟时,标准数值求解器在复杂孔隙域中收敛缓慢。本文提出一种基于神经网络的框架,直接从样品几何结构预测孔隙尺度速度场。方法采用带跳跃连接的卷积编码器-解码器架构,在提取多尺度特征的同时保留空间细节。通过自定义损失函数(包含速度重建、不可压缩性、固体内部无流速、周期性约束及全局曲折度指数一致性)促进物理一致性。分析了各损失权重的影响,并量化了各组件对预测精度的贡献。评估了多种CNN主干网络以确定准确且鲁棒的架构。在超出训练分布的样本上测试模型泛化能力,涵盖障碍物形状、边界条件、孔隙率变化及真实多孔结构。最后,展示利用预测速度场作为格子玻尔兹曼模拟初始条件的实用场景,该‘热启动’策略显著加速求解器收敛,在超过90%的测试案例中减少迭代次数。
原文摘要 · Abstract (English)
Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly in intricate porous domains. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method uses a convolutional encoder-decoder architecture with skip connections to preserve spatial detail while extracting multi-scale features. Physical consistency is encouraged through a custom loss function combining velocity reconstruction with incompressibility, no-flow conditions inside solids, periodicity constraints, and agreement with the global tortuosity index. We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy. Several CNN backbones are evaluated to identify architectures providing accurate and robust predictions. The generalization ability of the trained model is tested on samples outside the training distribution, including changes in obstacle geometry, boundary conditions, porosity, and realistic porous structures. Finally, we demonstrate a practical use of the predicted velocity fields as initial conditions for Lattice-Boltzmann simulations. This warm-start strategy accelerates solver convergence, reducing the number of iterations in over 90% of tested cases.
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