MAGNET: an open-source library for mesh agglomeration by Graph Neural Networks

Abstract

We introduce MAGNET, an open-source Python library designed for mesh agglomeration in both two- and three-dimensions, based on employing Graph Neural Networks (GNN). MAGNET serves as a comprehensive solution for training a variety of GNN models, integrating deep learning and other advanced algorithms such as METIS and k-means to facilitate mesh agglomeration and quality metric computation. The library's introduction is outlined through its code structure and primary features. The GNN framework adopts a graph bisection methodology that capitalizes on connectivity and geometric mesh information via SAGE convolutional layers, in line with the methodology proposed by Antonietti et al. (2024). Additionally, the proposed MAGNET library incorporates reinforcement learning to enhance the accuracy and robustness of the model for predicting coarse partitions within a multilevel framework. A detailed tutorial is provided to guide the user through the process of mesh agglomeration and the training of a GNN bisection model. We present several examples of mesh agglomeration conducted by MAGNET, demonstrating the library's applicability across various scenarios. Furthermore, the performance of the newly introduced models is contrasted with that of METIS and k-means, illustrating that the proposed GNN models are competitive regarding partition quality and computational efficiency. Finally, we exhibit the versatility of MAGNET's interface through its integration with Lymph, an open-source library implementing discontinuous Galerkin methods on polytopal grids for the numerical discretization of multiphysics differential problems.