Physics Informed Deep Learning for Flow and Transport in Porous Media
Physics Informed Deep Learning for Flow and Transport in Porous Media
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DOI：
10.2118/203934-ms
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发表时间：
2021-04
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通讯作者：
Cedric Fraces Gasmi;H. Tchelepi
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作者：
Cedric Fraces Gasmi;H. Tchelepi
本文介绍了物理信息深度学习在油藏模拟问题中的应用进展。该模型是一个神经网络，它经过联合训练，以尊重支配物理规律并匹配边界条件。该方法被用来模拟两相不相容运输问题(Buckley-Leverett)。该模型能够产生精确的激波和稀疏性物理解，并遵守控制偏微分方程式以及初始条件和边界条件。我们测试了各种假设(均匀和非均匀初始条件)，并表明在适当实施物理约束的情况下，可以在合理的时间和迭代内训练出健壮的解。我们回顾了以前工作[1]中提出的一些限制，并进一步讨论了该方法在正向纯双曲型系统中的适用性。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。我们回顾了文献中介绍的各种网络体系结构，并展示了有助于提高其收敛和准确性的提示。所提出的方法是一种向机器学习算法灌输物理知识的简单而优雅的方法。这缓解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。提出的原理可以在未来以无数种方式推广，并将导致一类新的算法来解决正向和反向物理问题。
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 [1] 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.