  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.
