Data driven discretizations for solving 2D advection problems

This repository contains the code used in the paper

Learned discretizations for passive scalar advection in a two dimensional turbulent flow. Jiawei Zhuang, Dmitrii Kochkov, Yohai Bar-Sinai, Michael P. Brenner, Stephan Hoyer. Physical Review Fluids, in print. arXiv: 2004.05477

This is an extension of the techniques developed in:

Learning data-driven discretizations for partial differential equations. Yohai Bar-Sinai*, Stephan Hoyer*, Jason Hickey, Michael P. Brenner. PNAS 2019, 116 (31) 15344-15349.

See this repository for the code used to produce results for the PNAS paper.

This is not an official Google product.

Installation

Installation is most easily done using pip.

1. Create or activate a virtual environment (e.g. using virtualenv or conda).

2. Install TensorFlow.

3. If you just want to install the package without the code, simply use pip to install directly from github:

   pip install git+git//github.com/google-research/data-driven-pdes

   If you want to fiddle around with the code, cd to where you want to store the code, clone the repo and install:

cd <your directory>
git clone git+https://github.com/google-research/data-driven-pdes
pip install -e data-driven-pdes

Usage

We aim to make the code accessible for researchers who want to apply our method to their favorite PDEs. To this end we wrote, and continue to write, tutorials and documentation. This is still very much in development, please open an issue if you have questions.

1. A tutorial notebook that explains some of the basic notions in the code base and demonstrates how to use the framework to define new equations.
2. This notebook contains a complete example of creating a training database, defining a model, training it and evaluating the trained model (well documented, though less pedagogical).