MAGNET: an open-source library for mesh agglomeration by graph neural networks

Abstract We introduce , an open-source Python library designed for mesh agglomeration in both two- and three-dimensions, based on employing Graph Neural Networks (GNN). 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 in (Antonietti and Manuzzi in J Comput Phys 452:110900, 2022; Antonietti et al. in Polytopal mesh agglomeration via geometrical deep learning for three-dimensional heterogeneous domains, arXiv:2406.10587 , 2024). Additionally, the proposed library incorporates reinforcement learning to enhance the accuracy and robustness of the model initially suggested in [1, 2] 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 , 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 ’s interface through its integration with , an open-source library implementing discontinuous Galerkin methods on polytopal grids for the numerical discretization of multiphysics differential problems.