# Graph Convolutional Networks for Simulating Multi-phase Flow and Transport in Porous Media

arXiv: https://arxiv.org/abs/2307.04449 · HTML: https://mlsanity.com/paper/2307.04449/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 10 Jul 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)
- [Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media](https://mlsanity.com/paper/1807.00882/) (2018)
- [Learning continuous-time PDEs from sparse data with graph neural networks](https://mlsanity.com/paper/2006.08956/) (2020)
- [CCSNet: a deep learning modeling suite for CO2 storage](https://mlsanity.com/paper/2104.01795/) (2021)
- [A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Media](https://mlsanity.com/paper/2105.02652/) (2021)
- [Learning time-dependent PDE solver using Message Passing Graph Neural Networks](https://mlsanity.com/paper/2204.07651/) (2022)

## Built on by (most cited first, 1 of 1)

- [Generative Latent Diffusion Model for Inverse Modeling and Uncertainty Analysis in Geological Carbon Sequestration](https://mlsanity.com/paper/2508.16640/) (2025)

## Abstract (arXiv)

Numerical simulation of multi-phase fluid dynamics in porous media is critical for many energy and environmental applications in Earth's subsurface. Data-driven surrogate modeling provides computationally inexpensive alternatives to high-fidelity numerical simulators. While the commonly used convolutional neural networks (CNNs) are powerful in approximating partial differential equation solutions, it remains challenging for CNNs to handle irregular and unstructured simulation meshes. However, simulation models for Earth's subsurface often involve unstructured meshes with complex mesh geometries, which limits the application of CNNs. To address this challenge, we construct surrogate models based on Graph Convolutional Networks (GCNs) to approximate the spatial-temporal solutions of multi-phase flow and transport processes in porous media. We propose a new GCN architecture suited to the hyperbolic character of the coupled PDE system, to better capture transport dynamics. Results of 2D heterogeneous test cases show that our surrogates predict the evolutions of pressure and saturation states with high accuracy, and the predicted rollouts remain stable for multiple timesteps. Moreover, the GCN-based models generalize well to irregular domain geometries and unstructured meshes that are unseen in the training dataset.