hp-Variational Physics-Informed Neural Networks for Nonlinear Two-Phase Transport in Porous Media
hp-Variational Physics-Informed Neural Networks for Nonlinear Two-Phase Transport in Porous Media
复制标题
用于多孔介质中非线性两相传输的 hp-变分物理神经网络
DOI：
10.1615/jmachlearnmodelcomput.2021038005
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
J. Foster
中科院分区：
文献类型：
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作者：
Mingyuan Yang;J. Foster
神经网络（NN）最近在解决各种计算物理问题方面引起了广泛关注。在本文中，我们重点关注使用 hp 变分物理信息神经网络 (hp-VPINNs) 方法来解决地下问题中的动态流体流动。该问题由具有初始条件和边界条件的非线性一阶双曲偏微分方程 (PDE) 控制。这个想法是训练一个代表解决方案的神经网络，以便在满足约束的同时遵守基本的物理定律。通过采用 hp -VPINNs 的方法，解决了前向问题，而无需在域内部添加任何额外的标记数据。它适用于偏微分方程中具有非凸通量函数的情况，其中解包含激波和混合波。此外，我们对问题进行了 HP 细化分析，并表明预细化是合适的，因为它解决了解决方案中的不连续性。最后，我们研究了逆两相输运问题并求解了非线性本构关系。使用稀疏测量作为先验知识，计算非线性本构关系，并获得整个计算域的解。
Neural networks (NN) have gained a lot attention recently in solving a wide range of computational physical problems. In this paper, we focus on solving a dynamic fluid-flow in a subsurface problem with the hp -variational physics-informed neural networks ( hp -VPINNs) approach. The problem is governed by a nonlinear first-order hyperbolic partial differential equation (PDE) with initial and boundary conditions. The idea is to train a neural network representing the solution such that the underlying physical laws are honored while the constraints are satisfied. By employing the approach of hp -VPINNs, the forward problem is solved without any additional labeled data in the interior of the domain. It works for a case with the nonconvex flux functions in the PDE, where the solution contains shocks and mixed waves. In addition, we performed hp refinement analysis on the problem and show that p refinement is suitable as it resolves the discontinuity in the solution. Finally, we investigated the inverse two-phase transport problem and solved for the nonlinear constitutive relation. With using sparse measurements as prior knowledge, the nonlinear constitutive relation was calculated and a solution over the entire computational domain was obtained.