Deep autoregressive neural networks for high-dimensional inverse problems

Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification

Shaoxing Mo, Nicholas Zabaras, Xiaoqing Shi, Jichun Wu

PyTorch implementation of deep autoregressive nueral networks based on a dense convolutional encoder-decoder network architecture for dynamical solute transport models with a time-varying source term and for subsequent high-dimensional inverse modeling. In the network, the time-varying process is represented using an autoregressive model, in which the time-dependent output at previous time step (y_i-1) is treated as input to predict the current output (y_i), that is,

y_i=f(x_i,y_i-1),

where x is the uncertain model input considered.

Dependencies

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

Datasets, Pretrained Model, and Forward Model Input Files

The datasets used have been uploaded to Google Drive and can be downloaded using this link https://drive.google.com/drive/folders/1CnITMyMOTmuSHQp8p5G9Vju3SFzi-9ae?usp=sharing

Training Data Shape

The training data are saved in the form: N x Nc x H x W, where N is the number of training samples, Nc is the number of input/output channels (i.e., the number of input/output fields considered), H x W is the spatial discretization resolution of the domain.

Network Training

With the training data prepared with the shape mentioned above, use the following command to train the network:

python train_Net.py   OR   python3 train_Net.py

One will need to change the 'data-dir' parameter, probably need to modify the values of kernel size, stride, zero padding in dense_ed.py according to the value of H x W (see Section 4.4 in Mo et al. (2019) for details).

Inverse Modeling

The iterative local updating ensemble smoother (ILUES) algorithm proposed in Zhang et al. (2018) is used in this study as the inversion framework to solve high-dimensional inverse problems. We would like to thank Dr. Zhang for sharing the codes of ILUES.

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 Zabaras, Nicholas and Shi, Xiaoqing and Wu, Jichun},
title = {Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant
         source identification},
journal = {Water Resources Research},
volume = {},
number = {},
pages = {},
year = {2019}
doi = {10.1029/2018WR024638},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018WR024638}
}

or:

Mo, S., Zabaras, N., Shi, X., & Wu, J. (2019). Deep autoregressive neural networks for high‐dimensional inverse
problems in groundwater contaminant source identification. Water Resources Research, 55. 
https://doi.org/10.1029/2018WR024638

Questions

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