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.

翻译：本研究探讨了受多重网格方法启发的神经算子架构——多重网格神经算子（MgNO）在多孔介质内多相流模拟中的应用。该架构经过调整，能够处理多种关键参数，如渗透率与孔隙度的非均质性。研究将MgNO扩展至时间相关的多孔介质流动问题，并验证了其在预测多相流关键特征方面的准确性。此外，本研究对MgNO与当前最流行的神经算子方法之一——傅里叶神经算子（FNO）进行了详细比较，重点分析两者在时间维度上预测误差累积的表现。这一比较为模型长期预测的稳定性与可靠性提供了重要见解。研究表明，MgNO能够有效模拟多相流问题，相较于传统模拟方法可显著节省计算时间，这标志着数据驱动方法在地球科学应用融合方面取得了重要进展。