arXiv 2104.026292021-04-22physics.flu-dyn

基于物理学的多孔介质流动与输运深度学习

Physics Informed Deep Learning for Flow and Transport in Porous Media

Cedric Fraces Gasmi, Hamdi Tchelepi

备注：: 19 pages, 17 figures. arXiv admin note: text overlap with arXiv:2001.05172 Thanks to Xin Ju for review and comments

摘要：

我们介绍了我们在将物理学深度学习应用于油藏模拟问题方面的进展。该模型是一个神经网络，它被联合训练以遵守管理物理定律并匹配边界条件。该方法在此用于模拟2相不混溶运输问题（巴克利-莱弗里特）。该模型能够产生一个精确的物理解，无论是在冲击和稀疏和荣誉的控制偏微分方程以及初始和边界条件。我们测试了各种假设（均匀和非均匀的初始条件），并表明通过适当的物理约束，可以在合理的时间和迭代内训练出一个强大的解决方案。我们重新审视了以前的工作\cite{Fuks2020}和进一步的适用性，这种方法在一个向前的，纯双曲线设置中提出的一些限制。我们还分享了一些关于物理信息神经网络（PINN）应用的实际发现。我们回顾了文献中提出的各种网络架构，并展示了有助于提高收敛性和准确性的提示。所提出的方法是一种简单而优雅的方式，可以将物理知识灌输给机器学习算法。这说明了机器学习算法的两个最重要的缺点：对大数据集的要求和外推的可靠性。提出的原则可以推广到无数的方式在未来，并应导致一类新的算法来解决正反物理问题。

英文摘要：

We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The methodology is hereby used to simulate a 2-phase immiscible transport problem (Buckley-Leverett). The model is able to produce an accurate physical solution both in terms of shock and rarefaction and honors the governing partial differential equation along with initial and boundary conditions. We test various hypothesis (uniform and non-uniform initial conditions) and show that with the proper implementation of physical constraints, a robust solution can be trained within a reasonable amount of time and iterations. We revisit some of the limitations presented in previous work \cite{Fuks2020} and further the applicability of this method in a forward, pure hyperbolic setup. We also share some practical findings on the application of physics informed neural networks (PINN). We review various network architectures presented in the literature and show tips that helped improve their convergence and accuracy. The proposed methodology is a simple and elegant way to instill physical knowledge to machine-learning algorithms. This alleviates the two most significant shortcomings of machine-learning algorithms: the requirement for large datasets and the reliability of extrapolation. The principles presented can be generalized in innumerable ways in the future and should lead to a new class of algorithms to solve both forward and inverse physical problems.

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。

摘要：

英文摘要：

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