A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media
A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media
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一种基于物理的分层正则化数据驱动模型，用于预测穿过多孔介质的流体流动
DOI：
10.1016/j.jcp.2021.110526
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
T. Germann
中科院分区：
文献类型：
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作者：
Kun Wang;Yu Chen;M. Mehana;N. Lubbers;K. Bennett;Q. Kang;H. Viswanathan;T. Germann
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，该网络能够从通过直接数值模拟流体通过孔隙结构产生的图像数据中学习，例如通过格子Boltzmann或分子动力学方法。与以往基于CAE的数据驱动方法相比，该模型的主要创新之处包括三个部分。第一种是将多孔介质的全域分解为子区域或“子域”的方法，以减小CAE的总体尺寸，并行批处理子域，并使CAE能够学习孔隙-流体速度的局部和可推广的非线性映射。第二种方法是将不可压缩的Navier-Stokes方程和连续性方程的有限差分解嵌入到CAE之前的卷积层中，以便为CAE提供流体动力学物理知识(PhyFlow)。第三个主要的新奇之处在于，CAE的训练是通过分层损失函数进行正则化的，该函数鼓励学习流体流动模式(以类似于主成分分析中的排序模式的方式)，从最重要到最不重要进行排序。这表明，这增加了学习的稳定性，减少了过拟合，并提高了CAE神经网络层(HierCAE)的可解释性。与传统的CAE模型相比，新的数据驱动模型PhyFlow-HierCAE模型表现出更高的精度和普适性，这归功于嵌入的物理知识和分层正则化，并且作为直接数值模拟的替代，在计算时间上实现了数量级的加速。提供了关于未见孔结构的训练和正向预测的例子，并对来自格子Boltzmann和孔隙流体流动的分子动力学模拟的数据进行了评估。该模型是一种快速、准确的模拟器(或“替代物”)，用于基于相对较小的直接数值模拟数据集的学习来预测未见孔结构的有效渗透率。
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 thePhyFlow-HierCAEmodel, 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.