# Towards Fast GNN Surrogates for CO2 Migration in Complex Geological Formations

arXiv: https://arxiv.org/abs/2606.17180 · HTML: https://mlsanity.com/paper/2606.17180/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 5 of 5)

- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition](https://mlsanity.com/paper/2507.08861/) (2025)
- [Learning CO2 plume migration in faulted reservoirs with Graph Neural Networks](https://mlsanity.com/paper/2306.09648/) (2023)

## Abstract (arXiv)

This chapter discusses how a data-driven machine learning approach can reproduce key aspects of the physical behavior of multiphase flows in complex geological formations. We propose an end-to-end graph neural surrogate tailored to CO2 plume migration forecasting in geological storage. The method is evaluated on the SPE11A benchmark, a well-known industry test case designed to assess CO2 storage scenarios and characterized by sharp gas-water interfaces, strong advective transport, and rapid convective mixing with fingering development. The benchmark is reformulated as a graph in which nodes represent computational cells and edges encode transmissibility-based interactions enriched with geometric attributes. Directional transport arising from grid geometry, permeability contrasts, and geological heterogeneity is captured through an anisotropic message-passing mechanism, where interaction weights are computed via geometry-conditioned edge embeddings, biasing message aggregation toward physically relevant transport directions. Temporal evolution is modeled in latent space using an autoregressive residual formulation trained with multi-step supervision. The proposed model produces competitive forecasts of gas saturation and liquid-phase density, which are key indicators for CO2 storage monitoring, with cumulative errors that remain moderate over extended forecasting horizons.