This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media. The architecture is adjusted to manage a variety of crucial factors, such as permeability and porosity heterogeneity. The study extendes MgNO to time-dependent porous media flow problems and validate its accuracy in predicting essential aspects of multiphase flows. Furthermore, the research provides a detailed comparison between MgNO and Fourier Neural Opeartor (FNO), which is one of the most popular neural operator methods, on their performance regarding prediction error accumulation over time. This aspect provides valuable insights into the models' long-term predictive stability and reliability. The study demonstrates MgNO's capability to effectively simulate multiphase flow problems, offering considerable time savings compared to traditional simulation methods, marking an advancement in integrating data-driven methodologies in geoscience applications.

该研究探讨了多重网格神经算子（MgNO）在多孔介质内多相流模拟中的应用，该架构针对各种关键因素进行了调整，如渗透率和孔隙率的异质性。该研究将MgNO扩展到依赖时间的多孔介质流动问题，并验证了其在预测多相流的关键方面的准确性。此外，研究还详细比较了MgNO和傅里叶神经算子（FNO），这是其中一种最流行的神经算子方法，它们在随时间积累预测误差方面的性能表现。该研究展示了MgNO有效地模拟多相流问题的能力，相比传统模拟方法节省了大量时间，这标志着数据驱动方法在地球科学应用中的进步。

多孔介质中多相流的MgNO方法