This repository is the official implementation of Deep Statistical Solvers (accepted at NeurIPS 2020).
The higher level ideas are located at the Graph Neural Solver paper (accepted at PSCC 2020).
The core idea is to address optimization problems with deep learning tools.
It is recommended to use a virtual environment, as it helps manage in a clean way the code dependencies.
pip install virtualenv
Go to the folder /DeepStatisticalSolver, and create a new virtualenv, with python 3
virtualenv ENV -p python3
The command above should have created a folder ENV/. Now you need to activate your virtual environment.
source ENV/bin/activate
You should now see (ENV) before your username. If you want to deactivate your virtualenv (for instance to work on another project), use the following command line
deactivate
But for now, keep you virtual environment activated!
If you have a GPU and want to use it, install the following requirements:
pip install -r requirements-gpu.txt
Otherwise, if you do not have a GPU, or do not want to use it, install the following requirements:
pip install -r requirements.txt
This work relies on datasets of optimization problems instances. We built these from scratch, and more informations are given in the notebooks. For each dataset, download all the files that are available at the links below, and place them in the corresponding folder:
- Dataset Linear systems --> place them in
datasets/linear_systems - Dataset AC power flow 14 nodes --> place them in
datasets/acpf_14 - Dataset AC power flow 118 nodes --> place them in
datasets/acpf_118
In the linear systems dataset, you also have to unzip the file varying_size.zip.
Disclaimer : In the submitted version of the paper Deep Statistical Solver, there are links to past versions of those datasets (with slight differences in file names, as well as in the problem.py files). Please use the most recent versions of the datasets by using the links above.
To train the models used in the paper, here are the exact commands that were used:
- Linear systems experiments
python main.py --data_dir=datasets/linear_systems --max_iter=1000000 --minibatch_size=100 --track_validation=1000 --learning_rate=1e-3 --discount=0.9 --latent_dimension=10 --hidden_layers=2 --correction_updates=30 --alpha=0.001
- AC power flow 14 nodes experiments
python main.py --data_dir=datasets/acpf_14 --learning_rate=3e-3 --minibatch_size=1000 --alpha=1e-2 --hidden_layers=2 --latent_dimension=10 --correction_updates=10 --track_validation=1000
- AC power flow 118 nodes experiments
python main.py --data_dir=datasets/acpf_118 --learning_rate=3e-3 --minibatch_size=500 --alpha=3e-4 --hidden_layers=2 --latent_dimension=10 --correction_updates=30 --track_validation=1000 --discount=0.9
To evaluate the models, we recommend to take a look at the jupyter notebooks. They provide some code to reload trained model, perform inference on the test set, and also some visualizations! See details below for more about the notebooks.
You can download pretrained models here.
Unzip the file and place all of the 9 model directories inside the DeepStatisticalSolver/results directory.
Here are the metrics for the three different experiments, and for each of the three corresponding models. The main metric is indeed the correlation with the best existing optimization method. Check the notebooks to obtain these results.
The best existing method is the LU decomposition.
| Model name | Model 0 | Model 1 | Model 2 |
|---|---|---|---|
| Correlation w/ LU | 99.99% | 99.99% | 99.99% |
| Loss 10th perc. | 3.0 E-4 | 3.8 E-4 | 2.7 E-4 |
| Loss median | 6.0 E-4 | 1.3 E-3 | 6.9 E-4 |
| Loss 90th perc. | 1.5 E-3 | 4.0 E-3 | 2.3 E-3 |
The best existing method is the Newton-Raphson method (NR). The correlation is in term of active power flows through power lines.
| Model name | Model 0 | Model 1 | Model 2 |
|---|---|---|---|
| Correlation w/ NR | 99.99% | 99.99% | 99.99% |
| Loss 10th perc. | 2.5 E-5 | 3.4 E-5 | 4.1 E-5 |
| Loss median | 4.0 E-5 | 6.3 E-5 | 1.0 E-4 |
| Loss 90th perc. | 1.0 E-4 | 1.5 E-4 | 4.4 E-4 |
The best existing method is the Newton-Raphson method (NR). The correlation is in term of active power flows through power lines.
| Model name | Model 0 | Model 1 | Model 2 |
|---|---|---|---|
| Correlation w/ NR | 99.99% | 99.99% | 99.99% |
| Loss 10th perc. | 5.3 E-7 | 1.3 E-6 | 1.7 E-7 |
| Loss median | 1.3 E-6 | 1.7 E-6 | 2.8 E-7 |
| Loss 90th perc. | 3.4 E-6 | 2.5 E-6 | 4.8 E-7 |
In order to help people understand and visualize our approach, we built a series of notebooks that provides visualizations and additional explanations about the problems and modelling choices. Feel free to take a look.
To do so, you need to open a jupyter notebook session:
ENV/bin/jupyter notebook
This should have opened a web page on your browser which allows you to naviguate through the directory. Click on the notebook/ folder, and then on the notebook you are interested in!