The simulation and prediction of fluid flow in porous media play a profoundly significant role in today's scientific and engineering domains, particularly in gaining a deeper understanding of phenomena such as the migration and fluid flow in underground rock formations and the enhancement of oil recovery rates. The flow of fluids in nanoscale porous media requires consideration of the effects of microscale phenomena, which are challenging to accurately describe using traditional physical models. Currently, research in deep learning for porous media predominantly focuses on conventional porous media, and there is an urgent need for investigations into heterogeneous nanoporous media. Simultaneously, there is a necessity to overcome the limitations of traditional data-driven models lacking physical prior knowledge. Therefore, the integration of physics-informed neural networks, which combine deep learning with physical principles, becomes essential for inferring relatively accurate results from sparse data. In this work, based on the heterogeneity of porous media in shale, we have introduced a deep learning model that couples physical information to predict the flow in heterogeneous nanoscale porous media. In the Physical Information Neural Network model, we utilize point clouds and couple them with deep residual networks. Discrete sampling points are used as inputs, and a multi-level residual connection, along with dimension concatenation, is employed to fuse feature information. The network, through backpropagation, takes into account the Navier-Stokes equations and wall conditions in heterogeneous nanoscale porous media. The results indicate that the apparent permeability and pressure field accuracy are over 90% and 95%, respectively. The Physical Information Neural Network demonstrates promising prospects for predicting flow in nanoscale porous media. Future work will extend to the multiphase complex flow in three-dimensional porous media.

中文翻译：

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基于物理信息神经网络的异质纳米多孔介质流动预测

多孔介质中流体流动的模拟和预测在当今的科学和工程领域中发挥着极其重要的作用，特别是在深入了解地下岩层中的运移和流体流动以及提高石油采收率等现象方面。纳米级多孔介质中的流体流动需要考虑微观现象的影响，而使用传统物理模型准确描述这些现象具有挑战性。目前，多孔介质深度学习的研究主要集中在传统多孔介质，迫切需要对异质纳米多孔介质进行研究。同时，有必要克服传统数据驱动模型缺乏物理先验知识的局限性。因此，将深度学习与物理原理相结合的物理信息神经网络的集成对于从稀疏数据推断相对准确的结果至关重要。在这项工作中，基于页岩中多孔介质的非均质性，我们引入了一种深度学习模型，该模型耦合物理信息来预测非均质纳米级多孔介质中的流动。在物理信息神经网络模型中，我们利用点云并将它们与深度残差网络耦合。使用离散采样点作为输入，并采用多级残差连接以及维度串联来融合特征信息。该网络通过反向传播，考虑了非均质纳米级多孔介质中的纳维-斯托克斯方程和壁面条件。结果表明，视渗透率和压力场精度分别超过90%和95%。物理信息神经网络展示了预测纳米级多孔介质流动的广阔前景。未来的工作将扩展到三维多孔介质中的多相复杂流动。