Recently, Kai Zhang's team summarized and reviewed the progress and challenges of integrating machine learning and traditional numerical algorithms in the field of numerical simulation of oil reservoirs, and the related research results were published in the journal Mathematics in the paper entitled "Progress and Challenges of Integrated Machine Learning and Traditional Numerical Algorithms: Taking Reservoir Numerical Simulation as an Example".

Innovation: Aiming at the hot issue of integrating machine learning methods with traditional numerical methods in the field of numerical simulation of oil reservoirs, the combination of traditional numerical methods with machine learning is reviewed. The article organizes the mainstream numerical methods nowadays, and summarizes the machine learning methods combined with numerical methods to solve the partial differential equations of reservoirs, elaborates on the application of machine learning methods in solving the partial differential equations of reservoirs, classifies and summarizes the mainstream deep learning methods for solving the partial differential equations of reservoirs, and looks forward to the future research directions and hot spots in this field.

Abstract: Machine learning techniques have garnered significant attention in various engineering disciplines due to their potential and benefits. Specifically, in reservoir numerical simulations, the core process revolves around solving the partial differential equations delineating oil, gas, and water flow dynamics in porous media. Discretizing these partial differential equations via numerical methods is one cornerstone of this simulation process. The synergy between traditional numerical methods and machine learning can enhance the precision of partial differential equation discretization. Moreover, machine learning algorithms can be employed to solve partial differential equations directly, yielding rapid convergence, heightened computational efficiency, and accuracies surpassing 95%. This manuscript offers an overview of the predominant numerical methods in reservoir simulations, focusing on integrating machine learning methodologies. The innovations in fusing deep learning techniques to solve reservoir partial differential equations are illuminated, coupled with a concise discussion of their inherent advantages and constraints. As machine learning continues to evolve, its conjunction with numerical methods is poised to be pivotal in addressing complex reservoir engineering challenges.

Mathematics (ISSN 2227-7390) specializes in publishing high-quality reviews, regular research papers, and short newsletters in all areas of pure and applied mathematics. In addition, Mathematics publishes timely and in-depth survey articles on current trends, new theoretical techniques, new ideas, and new mathematical tools in different branches of mathematics. The journal has a latest impact factor of 2.4, an average impact factor IF of 2.3 in the last 5 years, a JCR partition of Q1, and a CAS Mathematics major category 3.

Paper link:

https://doi.org/10.3390/math11214418

Citation:

Chen X, Zhang K, Ji Z, et al. Progress and Challenges of Integrated Machine Learning and Traditional Numerical Algorithms: Taking Reservoir Numerical Simulation as an Example[J]. Mathematics, 2023, 11(21): 4418.