In this work, a data-driven surrogate to high-fidelity numerical simulations is developed that can replace the numerical simulations of porous media. By learning the communications among grid cells in the numerical domain, this model is capable of accurately predicting flow fields for new sets of simulation runs. Because of the many possible random arrangements of particles and their orientation with respect to each other, generalization of permeability with high accuracy is not trivial - nor is it practical using conventional means. Furthermore, building a comprehensive data base for different grain/pore arrangements is not possible because of the cost of running numerical simulations to generate the data base that represent all possible arrangements. The objective is to predict grid-level flow fields in porous media as a priori to determining permeability of porous media. This work is continuation of our previous research. The rationale is that once the detailed grid-level dynamics can be accurately predicted using data-driven approach, for any configuration/topology of the porous media, the detailed dynamics could be predicted without any need for new expensive new numerical simulation runs. In this work, we improved previous work by accurately predicting permeability of the porous media, irrespective of the grain density, pore/grain shape, with significant reduction in computational time as opposed to previous work which was limited to a unique grain shape/size. The surrogate model is developed by employing a deep learning technique using the results of running high-fidelity numerical simulations for two-dimensional porous media consisting of circular grains, generated by varying the number and size of the circular solid grains. Robustness of the developed model is then tested for numerous variations of porous media - generated by varying the number and size of the solid grain angularity and elongation - which have not been used for developing the model. The deep convolutional neural network employed in this work is a combination of deep U-Net and ResNet structures to capture context and enable precise localization with avoiding issues in training caused by vanishing gradients.

在这项工作中，开发了一种数据驱动的高保真数值模拟替代方法，可以替代多孔介质的数值模拟。通过学习数值域中网格单元之间的通信，该模型能够准确预测新的模拟运行集的流场。由于粒子的许多可能的随机排列及其相对于彼此的方向，高精度的渗透率概括并非易事 - 使用常规方法也不实用。此外，由于运行数值模拟以生成代表所有可能排列的数据库的成本，因此不可能为不同的晶粒/孔隙排列建立综合数据库。目标是预测多孔介质中的网格级流场，作为确定多孔介质渗透率的先验。这项工作是我们之前研究的延续。基本原理是，一旦可以使用数据驱动的方法准确预测详细的网格级动力学，对于多孔介质的任何配置/拓扑，都可以预测详细的动力学，而无需进行新的昂贵的新数值模拟运行。在这项工作中，我们通过准确预测多孔介质的渗透率来改进以前的工作，而与颗粒密度、孔隙/颗粒形状无关，与以前仅限于独特颗粒形状/尺寸的工作相比，计算时间显着减少。替代模型是通过采用深度学习技术开发的，该技术使用对由圆形颗粒组成的二维多孔介质运行高保真数值模拟的结果，通过改变圆形固体颗粒的数量和尺寸生成。然后针对多孔介质的多种变化（通过改变固体颗粒角度和伸长率的数量和尺寸产生）测试开发模型的稳健性，这些变化尚未用于开发模型。这项工作中使用的深度卷积神经网络是深度 U-Net 和 ResNet 结构的组合，用于捕获上下文并实现精确定位，同时避免由梯度消失引起的训练问题。通过改变圆形固体颗粒的数量和大小产生。然后针对多孔介质的多种变化（通过改变固体颗粒角度和伸长率的数量和尺寸产生）测试开发模型的稳健性，这些变化尚未用于开发模型。这项工作中使用的深度卷积神经网络是深度 U-Net 和 ResNet 结构的组合，用于捕获上下文并实现精确定位，同时避免由梯度消失引起的训练问题。通过改变圆形固体颗粒的数量和大小产生。然后针对多孔介质的多种变化（通过改变固体颗粒角度和伸长率的数量和尺寸产生）测试开发模型的稳健性，这些变化尚未用于开发模型。这项工作中使用的深度卷积神经网络是深度 U-Net 和 ResNet 结构的组合，用于捕获上下文并实现精确定位，同时避免由梯度消失引起的训练问题。