# Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator

arXiv: https://arxiv.org/abs/2206.07680 · HTML: https://mlsanity.com/paper/2206.07680/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 15 Jun 2022.

## Builds on (most cited first, 10 of 10)

- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)
- [Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem](https://mlsanity.com/paper/2001.05172/) (2020)

## Built on by (most cited first, 15 of 15)

- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks](https://mlsanity.com/paper/2303.07310/) (2023)
- [Graph Network Surrogate Model for Subsurface Flow Optimization](https://mlsanity.com/paper/2312.08625/) (2023)
- [Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2406.03789/) (2024)
- [A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems](https://mlsanity.com/paper/2208.04995/) (2022)
- [Learning CO2 plume migration in faulted reservoirs with Graph Neural Networks](https://mlsanity.com/paper/2306.09648/) (2023)
- [Model-Agnostic AI Framework with Explicit Time Integration for Long-Term Fluid Dynamics Prediction](https://mlsanity.com/paper/2412.05657/) (2024)
- [A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling](https://mlsanity.com/paper/2506.07969/) (2025)
- [Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systems](https://mlsanity.com/paper/2602.11208/) (2026)
- [Learning Pore-scale Multi-phase Flow from Experimental Data with Graph Neural Network](https://mlsanity.com/paper/2411.14192/) (2024)
- [Learning multi-phase flow and transport in fractured porous media with auto-regressive and recurrent graph neural networks](https://mlsanity.com/paper/2502.17512/) (2025)
- [Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation](https://mlsanity.com/paper/2510.24216/) (2025)
- [Interventional Flow Matching: Prospective Dose-Response Forecasting with Velocity-Field Jacobian Regularization](https://mlsanity.com/paper/2606.29386/) (2026)
- [TRACE: A spatiotemporal contact memory graph network simulator for granular dynamics](https://mlsanity.com/paper/2609.02991/) (2026)
- [TWIG: A Time-Causal Wavelet Operator for Autoregressive Forecasting on Irregular Graphs](https://mlsanity.com/paper/2609.22585/) (2026)

## Abstract (arXiv)

Subsurface simulations use computational models to predict the flow of fluids (e.g., oil, water, gas) through porous media. These simulations are pivotal in industrial applications such as petroleum production, where fast and accurate models are needed for high-stake decision making, for example, for well placement optimization and field development planning. Classical finite difference numerical simulators require massive computational resources to model large-scale real-world reservoirs. Alternatively, streamline simulators and data-driven surrogate models are computationally more efficient by relying on approximate physics models, however they are insufficient to model complex reservoir dynamics at scale. Here we introduce Hybrid Graph Network Simulator (HGNS), which is a data-driven surrogate model for learning reservoir simulations of 3D subsurface fluid flows. To model complex reservoir dynamics at both local and global scale, HGNS consists of a subsurface graph neural network (SGNN) to model the evolution of fluid flows, and a 3D-U-Net to model the evolution of pressure. HGNS is able to scale to grids with millions of cells per time step, two orders of magnitude higher than previous surrogate models, and can accurately predict the fluid flow for tens of time steps (years into the future). Using an industry-standard subsurface flow dataset (SPE-10) with 1.1 million cells, we demonstrate that HGNS is able to reduce the inference time up to 18 times compared to standard subsurface simulators, and that it outperforms other learning-based models by reducing long-term prediction errors by up to 21%.