# Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media

arXiv: https://arxiv.org/abs/1807.00882 · HTML: https://mlsanity.com/paper/1807.00882/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2018.

## Built on by (most cited first, 30 of 56)

- [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)
- [Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains](https://mlsanity.com/paper/2104.10873/) (2021)
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- [Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models](https://mlsanity.com/paper/2107.09814/) (2021)
- [A Deep Learning-Accelerated Data Assimilation and Forecasting Workflow for Commercial-Scale Geologic Carbon Storage](https://mlsanity.com/paper/2105.09468/) (2021)
- [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)
- [Physics-informed neural networks for solving parametric magnetostatic problems](https://mlsanity.com/paper/2202.04041/) (2022)
- [Deep-learning-based coupled flow-geomechanics surrogate model for CO2 sequestration](https://mlsanity.com/paper/2105.01334/) (2021)
- [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)
- [A Physics-Constrained Deep Learning Model for Simulating Multiphase Flow in 3D Heterogeneous Porous Media](https://mlsanity.com/paper/2105.09467/) (2021)
- [Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2401.16683/) (2024)
- [Surrogate and inverse modeling for two-phase flow in porous media via theory-guided convolutional neural network](https://mlsanity.com/paper/2110.10080/) (2021)
- [Multi-fidelity Fourier Neural Operator for Fast Modeling of Large-Scale Geological Carbon Storage](https://mlsanity.com/paper/2308.09113/) (2023)
- [History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization](https://mlsanity.com/paper/2310.03228/) (2023)
- [Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media](https://mlsanity.com/paper/2405.19019/) (2024)
- [Bayesian neural networks for predicting uncertainty in full-field material response](https://mlsanity.com/paper/2406.14838/) (2024)
- [Weak neural variational inference for solving Bayesian inverse problems without forward models: applications in elastography](https://mlsanity.com/paper/2407.20697/) (2024)
- [VI-DGP: A variational inference method with deep generative prior for solving high-dimensional inverse problems](https://mlsanity.com/paper/2302.11173/) (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)
- [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)
- [Attention U-Net as a surrogate model for groundwater prediction](https://mlsanity.com/paper/2204.04518/) (2022)
- [AI-enhanced iterative solvers for accelerating the solution of large scale parametrized systems](https://mlsanity.com/paper/2207.02543/) (2022)
- [Learning CO2 plume migration in faulted reservoirs with Graph Neural Networks](https://mlsanity.com/paper/2306.09648/) (2023)
- [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)
- [Transfer Learning on Multi-Dimensional Data: A Novel Approach to Neural Network-Based Surrogate Modeling](https://mlsanity.com/paper/2410.12241/) (2024)
- [Walsh-Hadamard Neural Operators for Solving PDEs with Discontinuous Coefficients](https://mlsanity.com/paper/2511.07347/) (2025)

## Abstract (arXiv)

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of dimensionality, the saturation discontinuity due to capillarity effects, and the time-dependence of the multi-output responses. In this paper, we propose a deep convolutional encoder-decoder neural network methodology to tackle these issues. The surrogate modeling task is transformed to an image-to-image regression strategy. This approach extracts high-level coarse features from the high-dimensional input permeability images using an encoder, and then refines the coarse features to provide the output pressure/saturation images through a decoder. A training strategy combining a regression loss and a segmentation loss is proposed in order to better approximate the discontinuous saturation field. To characterize the high-dimensional time-dependent outputs of the dynamic system, time is treated as an additional input to the network that is trained using pairs of input realizations and of the corresponding system outputs at a limited number of time instances. The proposed method is evaluated using a geological carbon storage process-based multiphase flow model with a 2500-dimensional stochastic permeability field. With a relatively small number of training data, the surrogate model is capable of accurately characterizing the spatio-temporal evolution of the pressure and discontinuous CO2 saturation fields and can be used efficiently to compute the statistics of the system responses.