Physics Informed Deep Learning for Flow and Transport in Porous Media

Abstract

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.

arXiv comment19 pages, 17 figures. arXiv admin note: text overlap with arXiv:2001.05172 Thanks to Xin Ju for review and comments

References in corpus (8)

• DGM: A deep learning algorithm for solving partial differential equations
• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• Fourier Neural Operator for Parametric Partial Differential Equations
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
• On the Spectral Bias of Neural Networks

Cited by in corpus (2)

• Uncovering near-wall blood flow from sparse data with physics-informed neural networks
• Physics-informed attention-based neural network for solving non-linear partial differential equations