标题： MAGNET：基于图神经网络的网格聚类开源库 显示英文标题

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

摘要： 我们介绍了MAGNET，一个开源的Python库，旨在基于图神经网络（GNN）进行二维和三维网格聚类。 MAGNET作为一个综合解决方案，用于训练各种GNN模型，并集成了深度学习和其他先进算法如METIS和k-means，以促进网格聚类和质量度量计算。 通过代码结构和主要功能概述了该库的引入。 GNN框架采用了一种图形二分法方法，通过SAGE卷积层利用连接性和几何网格信息，与Antonietti等人（2024）提出的方法一致。 此外，所提出的MAGNET库结合了强化学习，以增强在多级框架内预测粗粒分区的模型的准确性和鲁棒性。 提供了一个详细的教程，指导用户完成网格聚类过程和GNN二分模型的训练。 我们展示了由MAGNET执行的几个网格聚类示例，证明了该库在各种场景中的适用性。 此外，新引入模型的性能与METIS和k-means进行了对比，表明所提出的GNN模型在分区质量和计算效率方面具有竞争力。 最后，我们通过将其与Lymph集成，展示了MAGNET界面的多功能性，Lymph是一个开源库，实现了多物理微分问题在多边形单元网格上的间断伽辽金方法的数值离散化。 显示英文摘要

摘要： 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.