利用自适应本构定律与神经网络预测高度非均质多孔介质中的非线性流动区域
Predicting nonlinear-flow regions in highly heterogeneous porous media using adaptive constitutive laws and neural networks
AI总结：
本文利用FP23自适应模型生成不同参数下的达西/达西-福希海默分区数据，训练神经网络对网格单元进行分类，从而加速高度非均质多孔介质中非线性流动区域的预测。
摘要：
在具有非均质渗透率的多孔介质中，可能会记录到范围广泛的流体速度，因此在高速区域可能产生显著的惯性效应和摩擦效应。在这些区域中，压力梯度与速度之间的关系通常通过达西定律建立，但该定律可能无法考虑这些效应；相反，引入非线性项的达西-福希海默定律可能更为适用。在整个求解域中全局应用达西-福希海默定律在数值上代价极高，因此只应在确有必要的地方使用。最近，FP23通过采用自适应模型回答了如何先验地确定应限制使用达西-福希海默定律的子域这一问题：给定一个流速阈值，该模型在求解过程中局部选择更合适的定律。求解结束时，每个网格单元被标记为属于达西子域或达西-福希海默子域。然而，该模型本身是非线性的，因此运行成本相对较高。在本文中，为了加速将求解域划分为低速和高速区域的过程，我们利用FP23中的自适应模型，针对不同的输入参数（如边界条件和惯性系数）数组生成分区数据，然后在这些数据上训练神经网络，将每个网格单元分类为达西或非达西。文中研究了两个测试算例以说明结果，并分析了代价函数、一致性图、精确率-召回率曲线和受试者工作特征曲线。
英文摘要：
In a porous medium featuring heterogeneous permeabilities, a wide range of fluid velocities may be recorded, so that significant inertial and frictional effects may arise in high-speed regions. In such parts, the link between pressure gradient and velocity is typically made via Darcy's law, which may fail to account for these effects; instead, the Darcy Forchheimer law, which introduces a nonlinear term, may be more adequate. Applying the Darcy Forchheimer law globally in the domain is very costly numerically and, rather, should only be done where strictly necessary. The question of finding a prori the subdomain where to restrict the use of the Darcy Forchheimer law was recently answered in FP23 by using an adaptive model: given a threshold on the flow velocity, the model locally selects the more appropriate law as it is being solved. At the end of the resolution, each mesh cell is flagged as being in the Darcy or Darcy Forchheimer subdomain. Still, this model is nonlinear itself and thus relatively expensive to run. In this paper, to accelerate the subdivision of the domain into low and high speed regions, we instead exploit the adaptive model from FP23 to generate partitioning data given an array of different input parameters, such as boundary conditions and inertial coefficients, and then train neural networks on these data classifying each mesh cell as Darcy or not. Two test cases are studied to illustrate the results, where cost functions, parity plots, precision-recall plots and receiver operating characteristic curves are analyzed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
