Uncertainty Quantification in the POD-NN framework

Source code from Non-intrusive reduced-order modeling using uncertainty-aware Deep Neural Networks and Proper Orthogonal Decomposition: application to Flood Modeling.

An overview of this work is available here.

Requires Python 3.6+. Dependencies are in the file requirements.txt on any branch, and are installable via pip (or pip3 if Python 3 isn’t the default one):

$ pip3 install -r requirements.txt

Running our POD-NN implementation (Wang et al., 2019)

Run experiments from their directories, eg.

$ git checkout POD-NN
$ cd experiments/2d_ackley
$ python3 main.py

Available experiments in experiments:

• 1d_shekel, the 1D Shekel function
• 2d_ackley, the 2D Ackley function
• 1dt_burger, a solution of the 1D, unsteady Burger’s Equation

Running the POD-EnsNN model (Uncertainty Quantification via Deep Ensembles)

$ git checkout POD-EnsNN
$ cd experiments/2d_ackley
$ python3 main.py

Or to distribute on a machine with 5 GPUs

$ python3 gen.py && horovodrun -np 5 -H localhost:5 python3 train.py --distribute && python3 pred.py

Available experiments in experiments:

• 1d_shekel, the 1D Shekel function
• 2d_ackley, the 2D Ackley function
• 1dt_burger, a solution of the 1D, unsteady Burger’s Equation
• 2d_shallowwater, Flood Modeling on simulations results from CuteFlow, solving 2D Shallow Water Equations
• 1dt_shallowwater, Dam Break test case, solving 1D, unsteady Shallow Water Equations
• 2dt_shallowwater, Dam Break simulations results from CuteFlow, solving 2D, unsteady Shallow Water Equations

Running the POD-BNN model (Uncertainty Quantification via Bayesian NN)

$ git checkout POD-BNN
$ cd experiments/2d_ackley
$ python3 main.py

Available experiments in experiments:

• 1d_shekel, the 1D Shekel function
• 2d_ackley, the 2D Ackley function
• 1dt_burger, a solution of the 1D, unsteady Burger’s Equation
• 2d_shallowwater: Flood Modeling on simulations results from CuteFlow, solving 2D Shallow Water Equations
• 1dt_shallowwater, Dam Break test case, solving 1D, unsteady Shallow Water Equations
• 2dt_shallowwater, Dam Break simulations results from CuteFlow, solving 2D, unsteady Shallow Water Equations

Runner files for Compute Canada clusters

For each branch, we provide experiments/runner.sh to run all simulations. It is meant to be used on Compute Canada clusters, such as Beluga, located at ÉTS. A Python 3.6+ environment at ~/env needs to contain the packages required in requirements.txt, plus horovod.

Citations

The preprint is out and can be cited as follows.

@misc{jacquier2020nonintrusive,
    title={Non-Intrusive Reduced-Order Modeling Using Uncertainty-Aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to Flood Modeling},
    author={Pierre Jacquier and Azzedine Abdedou and Vincent Delmas and Azzeddine Soulaimani},
    year={2020},
    eprint={2005.13506},
    archivePrefix={arXiv},
    primaryClass={physics.comp-ph}
}

This work is building on techniques from Wang et al.

@article{Wang2019,
author = {Wang, Qian and Hesthaven, Jan S. and Ray, Deep},
doi = {10.1016/J.JCP.2019.01.031},
issn = {0021-9991},
journal = {Journal of Computational Physics},
month = {may},
pages = {289--307},
publisher = {Academic Press},
title = {{Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem}},
url = {https://www.sciencedirect.com/science/article/pii/S0021999119300828},
volume = {384},
year = {2019}
}

License

MIT License

Copyright (c) 2020 Pierre Jacquier