# A MgNO Method for Multiphase Flow in Porous Media

arXiv: https://arxiv.org/abs/2407.02505 · HTML: https://mlsanity.com/paper/2407.02505/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 16 Jun 2024.

## Builds on (most cited first, 8 of 8)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Mitigating spectral bias for the multiscale operator learning](https://mlsanity.com/paper/2210.10890/) (2022)
- [MgNet: A Unified Framework of Multigrid and Convolutional Neural Network](https://mlsanity.com/paper/1901.10415/) (2019)
- [MgNO: Efficient Parameterization of Linear Operators via Multigrid](https://mlsanity.com/paper/2310.19809/) (2023)
- [An Enhanced V-cycle MgNet Model for Operator Learning in Numerical Partial Differential Equations](https://mlsanity.com/paper/2302.00938/) (2023)

## Built on by (most cited first, 2 of 2)

- [Recurrent Neural Operators: Stable Long-Term PDE Prediction](https://mlsanity.com/paper/2505.20721/) (2025)
- [PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations](https://mlsanity.com/paper/2506.01598/) (2025)

## Abstract (arXiv)

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.