Deep Convolutional Encoder-Decoder Networks for Dynamical Multi-Phase Flow Models

Deep Convolutional Encoder-Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media

Shaoxing Mo, Yinhaozhu, Nicholas Zabaras, Xiaoqing Shi, Jichun Wu

PyTorch implementation of deep convolutional nueral networks for dynamical multi-phase flow models with discontinuous outputs and for subsequent uncertainty quantification. We treat time as an input to network to predict the time-dependent outputs of the dynamic system.

The first column is the forward model predictions for the pressure (left) and discontinuous saturation (right) fields at t=100, 150, and 200 days. The second and third columns are the network predictions and predicted errors, respectively.

Two-Stage Network Training Combining Regression and Segmentation Losses

To improve the approximation accuracy for the irregular discontinuous saturation front, we binarize (0 or 1) the saturation field and the resulting image is added as an additional output channel to the network. A binary cross entropy (BCE) loss is used for the the two-class segmentation task (CNN-MSE-BCE loss). The network with a MSE loss (CNN-MSE loss) solely is also provided for comparison. Left: Discontinuous saturation field. Right: The corrresponding binarized image.

Network Architecture

The network is fully convolutional without any fully-connnected layers and is an alternation of dense blocks and transition (encoding/decoding) layers.

Dependencies

• python 3
• PyTorch 0.4
• h5py
• matplotlib
• seaborn

Datasets, Pretrained Model, and Forward Model Input Files

The datasets used, pretrained models, input files for the forward model, and needed scripts have been uploaded to Google Drive and can be downloaded using this link https://drive.google.com/drive/folders/1keg9HwP3bs9JUCyqYflKNwIHwep2CD6r?usp=sharing

Repo Structure

Illustration of the repo structure. The training data are obtained by reorganizing the original data (see Section 3.3 in Mo et al. (2019)) to characterize the system dynamics.

Start with a Pre-trained Model

The pretrained models of networks with the MSE loss and with the MSE-BCE loss are available on Google Drive. One can plot the images provided using the script "post_usePretrainedModel.py".

Network Training

python3 train_time.py

Citation

See Mo et al. (2019) for more information. If you find this repo useful for your research, please consider to cite:

@article{moetal2019,
author = {Mo, Shaoxing and Zhu, Yinhao and Zabaras, Nicholas, J and Shi, Xiaoqing and Wu, Jichun},
title = {Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media},
journal = {Water Resources Research},
volume = {55},
number = {1},
pages = {703-728},
year = {2019},
keywords = {Multiphase flow, geological carbon storage, uncertainty quantification, deep neural networks, high-dimensionality, response discontinuity},
doi = {10.1029/2018WR023528},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018WR023528},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2018WR023528},
}

or:

Mo, S., Zhu, Y., Zabaras, N. J., Shi, X., & Wu, J. (2019). Deep convolutional encoder‐decoder networks for
uncertainty quantification of dynamic multiphase flow in heterogeneous media. Water Resources Research, 
55, 703– 728. https://doi.org/10.1029/2018WR023528

Related article: Zhu, Y., & Zabaras, N. (2018). Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification. J. Comput. Phys., 366, 415-447.

Questions

Contact Shaoxing Mo (smo@smail.nju.edu.cn) or Nicholas Zabaras (nzabaras@gmail.com) with questions or comments.