# A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems

arXiv: https://arxiv.org/abs/1908.05823 · HTML: https://mlsanity.com/paper/1908.05823/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Aug 2019.

## Built on by (most cited first, 30 of 59)

- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [Transfer Learning on Multi-Fidelity Data](https://mlsanity.com/paper/2105.00856/) (2021)
- [Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers](https://mlsanity.com/paper/2103.09360/) (2021)
- [Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator](https://mlsanity.com/paper/2206.07680/) (2022)
- [A Deep Learning-Accelerated Data Assimilation and Forecasting Workflow for Commercial-Scale Geologic Carbon Storage](https://mlsanity.com/paper/2105.09468/) (2021)
- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [CCSNet: a deep learning modeling suite for CO2 storage](https://mlsanity.com/paper/2104.01795/) (2021)
- [Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems](https://mlsanity.com/paper/2102.03169/) (2021)
- [Use of Multifidelity Training Data and Transfer Learning for Efficient Construction of Subsurface Flow Surrogate Models](https://mlsanity.com/paper/2204.11138/) (2022)
- [Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration](https://mlsanity.com/paper/2409.16572/) (2024)
- [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)
- [Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology](https://mlsanity.com/paper/2203.13375/) (2022)
- [A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Media](https://mlsanity.com/paper/2105.02652/) (2021)
- [Surrogate Modeling of Melt Pool Thermal Field using Deep Learning](https://mlsanity.com/paper/2207.12259/) (2022)
- [Deep-learning-based coupled flow-geomechanics surrogate model for CO2 sequestration](https://mlsanity.com/paper/2105.01334/) (2021)
- [A Physics-Constrained Deep Learning Model for Simulating Multiphase Flow in 3D Heterogeneous Porous Media](https://mlsanity.com/paper/2105.09467/) (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)
- [Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles](https://mlsanity.com/paper/2302.09748/) (2023)
- [Convolutional-Recurrent Neural Network Proxy for Robust Optimization and Closed-Loop Reservoir Management](https://mlsanity.com/paper/2203.07524/) (2022)
- [Physics-informed Convolutional Recurrent Surrogate Model for Reservoir Simulation with Well Controls](https://mlsanity.com/paper/2305.09056/) (2023)
- [Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls](https://mlsanity.com/paper/2310.06319/) (2023)
- [Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2406.03789/) (2024)
- [Machine Learning in Heterogeneous Porous Materials](https://mlsanity.com/paper/2202.04137/) (2022)
- [Learning CO2 plume migration in faulted reservoirs with Graph Neural Networks](https://mlsanity.com/paper/2306.09648/) (2023)
- [High Throughput Training of Deep Surrogates from Large Ensemble Runs](https://mlsanity.com/paper/2309.16743/) (2023)
- [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)

## Abstract (arXiv)

A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures, specifically a residual U-Net and a convolutional long short term memory recurrent network. Training samples entail global pressure and saturation maps, at a series of time steps, generated by simulating oil-water flow in many (1500 in our case) realizations of a 2D channelized system. After training, the `recurrent R-U-Net' surrogate model is shown to be capable of accurately predicting dynamic pressure and saturation maps and well rates (e.g., time-varying oil and water rates at production wells) for new geological realizations. Assessments demonstrating high surrogate-model accuracy are presented for an individual geological realization and for an ensemble of 500 test geomodels. The surrogate model is then used for the challenging problem of data assimilation (history matching) in a channelized system. For this study, posterior reservoir models are generated using the randomized maximum likelihood method, with the permeability field represented using the recently developed CNN-PCA parameterization. The flow responses required during the data assimilation procedure are provided by the recurrent R-U-Net. The overall approach is shown to lead to substantial reduction in prediction uncertainty. High-fidelity numerical simulation results for the posterior geomodels (generated by the surrogate-based data assimilation procedure) are shown to be in essential agreement with the recurrent R-U-Net predictions. The accuracy and dramatic speedup provided by the surrogate model suggest that it may eventually enable the application of more formal posterior sampling methods in realistic problems.