# Accelerated training of deep learning surrogate models for surface displacement and flow, with application to MCMC-based history matching of CO2 storage operations

arXiv: https://arxiv.org/abs/2408.10717 · HTML: https://mlsanity.com/paper/2408.10717/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operators](https://mlsanity.com/paper/2210.17051/) (2022)
- [3D CNN-PCA: A Deep-Learning-Based Parameterization for Complex Geomodels](https://mlsanity.com/paper/2007.08478/) (2020)
- [Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Models](https://mlsanity.com/paper/2204.11138/) (2022)
- [A Robust Deep Learning Workflow to Predict Multiphase Flow Behavior during Geological CO2 Sequestration Injection and Post-Injection Periods](https://mlsanity.com/paper/2107.07274/) (2021)
- [Markov Chain Monte Carlo with Neural Network Surrogates: Application to Contaminant Source Identification](https://mlsanity.com/paper/2003.02322/) (2020)
- [Surrogate Model for Geological CO2 Storage and Its Use in Hierarchical MCMC History Matching](https://mlsanity.com/paper/2308.06341/) (2023)
- [Dimension-Robust MCMC in Bayesian Inverse Problems](https://mlsanity.com/paper/1803.03344/) (2018)
- [Deep Learning-Accelerated 3D Carbon Storage Reservoir Pressure Forecasting Based on Data Assimilation Using Surface Displacement from InSAR](https://mlsanity.com/paper/2201.08543/) (2022)
- [AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage](https://mlsanity.com/paper/2402.06110/) (2024)
- [Multigrid reduction preconditioning framework for coupled processes in porous and fractured media](https://mlsanity.com/paper/2101.11649/) (2021)
- [History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization](https://mlsanity.com/paper/2310.03228/) (2023)
- [Graph Network Surrogate Model for Subsurface Flow Optimization](https://mlsanity.com/paper/2312.08625/) (2023)

## Built on by (most cited first, 3 of 3)

- [Deep operator network for surrogate modeling of poroelasticity with random permeability fields](https://mlsanity.com/paper/2509.11966/) (2025)
- [Machine learning for sustainable geoenergy: uncertainty, physics and decision-ready inference](https://mlsanity.com/paper/2603.14907/) (2026)
- [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)

Deep learning surrogate modeling shows great promise for subsurface flow applications, but the training demands can be substantial. Here we introduce a new surrogate modeling framework to predict CO2 saturation, pressure and surface displacement for use in the history matching of carbon storage operations. Rather than train using a large number of expensive coupled flow-geomechanics simulation runs, training here involves a large number of inexpensive flow-only simulations combined with a much smaller number of coupled runs. The flow-only runs use an effective rock compressibility, which is shown to provide accurate predictions for saturation and pressure for our system. A recurrent residual U-Net architecture is applied for the saturation and pressure surrogate models, while a new residual U-Net model is introduced to predict surface displacement. The surface displacement surrogate accepts, as inputs, geomodel quantities along with saturation and pressure surrogate predictions. Median relative error for a diverse test set is less than 4% for all variables. The surrogate models are incorporated into a hierarchical Markov chain Monte Carlo history matching workflow. Surrogate error is included using a new treatment involving the full model error covariance matrix. A high degree of prior uncertainty, with geomodels characterized by uncertain geological scenario parameters (metaparameters) and associated realizations, is considered. History matching results for a synthetic true model are generated using in-situ monitoring-well data only, surface displacement data only, and both data types. The enhanced uncertainty reduction achieved with both data types is quantified. Posterior saturation and surface displacement fields are shown to correspond well with the true solution.