This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

本文提出了一种新的深度学习数据驱动模型，用于预测岩石中结构相关的孔隙流体速度场。该模型基于卷积自动编码器 (CAE) 人工神经网络，能够从通过孔隙结构的流体流动的直接数值模拟生成的图像数据中学习，例如通过格子玻尔兹曼或分子动力学方法。与以前基于 CAE 的数据驱动方法相比，该模型的主要新颖之处包括三个部分。第一个是将多孔介质的全域分解为子区域或“子域”的方法，以减少 CAE 的整体大小，并行批处理子域，并使CAE 学习局部和可推广的孔隙流体速度非线性映射。物理流）。第三个主要新颖之处在于，CAE 的训练通过分层损失函数进行正则化，该函数鼓励学习流体流动模式（类似于主成分分析中的排序模式），从最重要到最不重要。这被证明可以提高学习的稳定性，减少过度拟合，并促进 CAE 神经网络层 ( HierCAE ) 的可解释性。全面的新数据驱动模型，我们称之为PhyFlow-HierCAE模型显示出比传统 CAE 模型更高的流场预测准确性和通用性，这归因于嵌入的物理知识和分层正则化，以及实现计算时间的数量级加速，作为直接数值计算的替代模拟。提供了对未知孔隙结构的训练和前向预测的示例，并评估了来自格子玻尔兹曼和孔隙流体流动的分子动力学模拟的数据。该模型被证明是一种快速而准确的模拟器（或“替代品”），用于基于从相对较小的直接数值模拟数据集中学习来预测未知孔隙结构的有效渗透率。