Torch_pdegraph

Torch_pdegraph is a proof of concept that how one can solve PDEs (partial difference equations) on graphs using the Message Passing class of torch_geometric and hence also benefits from the hardware acceleration. See the video-presentation

What is a PDE on a graph?

The basic idea is that one can define the operators like, derivatives, gradients, laplacians on graphs and construct a PDE inspired from nature on graphs. To know more about PDEs on graph.

• See the publications of Elmoataz.
• See also their applications on pointclouds
• Classical PDEs on images by Guillermo Sapiro
• Be sure to play with the jupyter-notebooks in the applications/ folder which presents few of their applications. Download the data
• Ref to operator_calculus.md for a brisk intro to calculus on graphs.

Installation

First install the torch_geometric. Then one can clone this project and install it locally:

pip install --upgrade pip
pip install .

Or do:

pip install --upgrade pip
pip install torch_pdegraph

Running the notebooks

In the notebooks I am demonstrating few applications of pdes on images and pcd by creating simple knn-graphs on gpu. One will need faiss library to create the graphs.

To display the pcds inside the notebook I am using jupyter visualization feature in open3d which uses a jupyter widget, notebooks must be running to for the widget to function.

To do:

• Add an interpolation application.
• Add a segmentation predefined pde.