# Graph Network Surrogate Model for Subsurface Flow Optimization

arXiv: https://arxiv.org/abs/2312.08625 · HTML: https://mlsanity.com/paper/2312.08625/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 15 of 15)

- [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)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
- [Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks](https://mlsanity.com/paper/2203.08852/) (2022)
- [Learning Controllable Adaptive Simulation for Multi-resolution Physics](https://mlsanity.com/paper/2305.01122/) (2023)
- [Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator](https://mlsanity.com/paper/2206.07680/) (2022)
- [Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology](https://mlsanity.com/paper/2203.13375/) (2022)
- [Deep-learning-based coupled flow-geomechanics surrogate model for CO2 sequestration](https://mlsanity.com/paper/2105.01334/) (2021)
- [Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network](https://mlsanity.com/paper/2110.10080/) (2021)
- [Use of low-fidelity models with machine-learning error correction for well placement optimization](https://mlsanity.com/paper/2111.02960/) (2021)
- [Convolutional-Recurrent Neural Network Proxy for Robust Optimization and Closed-Loop Reservoir Management](https://mlsanity.com/paper/2203.07524/) (2022)
- [Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder network](https://mlsanity.com/paper/2111.08691/) (2021)

## Built on by (most cited first, 4 of 4)

- [Deep Learning Framework for History Matching CO2 Storage with 4D Seismic and Monitoring Well Data](https://mlsanity.com/paper/2408.01575/) (2024)
- [Accelerated training of deep learning surrogate models for surface displacement and flow, with application to MCMC-based history matching of CO2 storage operations](https://mlsanity.com/paper/2408.10717/) (2024)
- [A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structures](https://mlsanity.com/paper/2503.22252/) (2025)
- [AutoSurrogate: An LLM-Driven Multi-Agent Framework for Autonomous Construction of Deep Learning Surrogate Models in Subsurface Flow](https://mlsanity.com/paper/2604.11945/) (2026)

## Abstract (arXiv)

The optimization of well locations and controls is an important step in the design of subsurface flow operations such as oil production or geological CO2 storage. These optimization problems can be computationally expensive, however, as many potential candidate solutions must be evaluated. In this study, we propose a graph network surrogate model (GNSM) for optimizing well placement and controls. The GNSM transforms the flow model into a computational graph that involves an encoding-processing-decoding architecture. Separate networks are constructed to provide global predictions for the pressure and saturation state variables. Model performance is enhanced through the inclusion of the single-phase steady-state pressure solution as a feature. A multistage multistep strategy is used for training. The trained GNSM is applied to predict flow responses in a 2D unstructured model of a channelized reservoir. Results are presented for a large set of test cases, in which five injection wells and five production wells are placed randomly throughout the model, with a random control variable (bottom-hole pressure) assigned to each well. Median relative error in pressure and saturation for 300 such test cases is 1-2%. The ability of the trained GNSM to provide accurate predictions for a new (geologically similar) permeability realization is demonstrated. Finally, the trained GNSM is used to optimize well locations and controls with a differential evolution algorithm. GNSM-based optimization results are comparable to those from simulation-based optimization, with a runtime speedup of a factor of 36. Much larger speedups are expected if the method is used for robust optimization, in which each candidate solution is evaluated on multiple geological models.