GNN-based Polygonal Grids Agglomeration

This repository contains the material related to the implementation of the GNN-based method introduced in the paper: Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers.

P. F. Antonietti, N. Farenga, E. Manuzzi, G. Martinelli, L. Saverio

Installation

To install python requirements run the command

pip install -r requirements.txt

However, a dedicated installation of the torch-geometric package is recommended, via

pip install torch-scatter -f https://data.pyg.org/whl/torch-{TORCH}+{CUDA}.html
pip install torch-sparse -f https://data.pyg.org/whl/torch-{TORCH}+{CUDA}.html
pip install torch-cluster -f https://data.pyg.org/whl/torch-{TORCH}+{CUDA}.html
pip install torch-spline-conv -f https://data.pyg.org/whl/torch-{TORCH}+{CUDA}.html
pip install torch-geometric

By replacing {TORCH} & {CUDA} with the installed torch and cuda versions, retrievable by running the python command torch.__version__.

Project structure

The folder structure is the following:

• dataset_generation contains the MATLAB scripts used for generating the meshes, extracting the graphs together with their features, and the concatenation scripts to bundle the data.

• training contains the python scripts used for the definition, tuning and training of the models, the trained models, and the runtime benchmarking test.

• code_agglom_MG contains the MATLAB code to perform agglomeration and numerical experiments (multigrid), with the different python wrappers to load the models within the code_agglom_MG/mesh/agglomerate folder.

  Note To load a specific model, the path to the trained model at line 7 of the file code_agglom_MG/mesh/agglomerate/aggl_GNN_fun.m, and the model's wrapper filename at line 21, have to be both updated.

Citation

@misc{antonietti2022agglomeration,
    title={Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers},
    author={P. F. Antonietti and N. Farenga and E. Manuzzi and G. Martinelli and L. Saverio},
    year={2022},
    eprint={2210.17457},
    archivePrefix={arXiv},
    primaryClass={math.NA}
    }