# Uncertainty quantification of two-phase flow in porous media via coupled-TgNN surrogate model

arXiv: https://arxiv.org/abs/2205.14301 · HTML: https://mlsanity.com/paper/2205.14301/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 44 references that are in the map.
- First posted on arXiv 28 May 2022.

## Builds on (most cited first, 11 of 11)

- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Deep Learning of Subsurface Flow via Theory-guided Neural Network](https://mlsanity.com/paper/1911.00103/) (2019)
- [Efficient Uncertainty Quantification for Dynamic Subsurface Flow with Surrogate by Theory-guided Neural Network](https://mlsanity.com/paper/2004.13560/) (2020)
- [A machine learning approach for efficient uncertainty quantification using multiscale methods](https://mlsanity.com/paper/1711.04315/) (2017)
- [A Deep-Learning-Based Geological Parameterization for History Matching Complex Models](https://mlsanity.com/paper/1807.02716/) (2018)
- [Integration of adversarial autoencoders with residual dense convolutional networks for estimation of non-Gaussian hydraulic conductivities](https://mlsanity.com/paper/1906.11828/) (2019)
- [Modeling nanoconfinement effects using active learning](https://mlsanity.com/paper/2005.02587/) (2020)
- [Computationally Efficient CFD Prediction of Bubbly Flow using Physics-Guided Deep Learning](https://mlsanity.com/paper/1910.08037/) (2019)

## Abstract (arXiv)

Uncertainty quantification (UQ) of subsurface two-phase flow usually requires numerous executions of forward simulations under varying conditions. In this work, a novel coupled theory-guided neural network (TgNN) based surrogate model is built to facilitate computation efficiency under the premise of satisfactory accuracy. The core notion of this proposed method is to bridge two separate blocks on top of an overall network. They underlie the TgNN model in a coupled form, which reflects the coupling nature of pressure and water saturation in the two-phase flow equation. The TgNN model not only relies on labeled data, but also incorporates underlying scientific theory and experiential rules (e.g., governing equations, stochastic parameter fields, boundary and initial conditions, well conditions, and expert knowledge) as additional components into the loss function. The performance of the TgNN-based surrogate model for two-phase flow problems is tested by different numbers of labeled data and collocation points, as well as the existence of data noise. The proposed TgNN-based surrogate model offers an effective way to solve the coupled nonlinear two-phase flow problem and demonstrates good accuracy and strong robustness when compared with the purely data-driven surrogate model. By combining the accurate TgNN-based surrogate model with the Monte Carlo method, UQ tasks can be performed at a minimum cost to evaluate statistical quantities. Since the heterogeneity of the random fields strongly impacts the results of the surrogate model, corresponding variance and correlation length are added to the input of the neural network to maintain its predictive capacity. The results show that the TgNN-based surrogate model achieves satisfactory accuracy, stability, and efficiency in UQ problems of subsurface two-phase flow.