论文标题
基于机器学习的精炼策略，用于多面体网格，应用于虚拟元素和多面体不连续的盖尔金方法
Machine Learning based refinement strategies for polyhedral grids with applications to Virtual Element and polyhedral Discontinuous Galerkin methods
论文作者
论文摘要
我们提出了两种基于机器学习技术来处理多面体网格细化的新策略，可以在自适应框架内使用。第一个采用K-均值聚类算法来划分要完善的多面体的点。该策略是众所周知的centroidal voronoi tessellation的变体。第二个采用卷积神经网络来对元素的“形状”进行分类，以便可以定义“临时”改进标准。该策略可用于以低的在线计算成本来增强现有的改进策略，包括K-Means策略。我们测试了提出的算法，这些算法考虑了两个有限元方法的家族，这些方法支持任意形状的多面体元素，即虚拟元素方法（VEM）和多边形不连续的Galerkin（Polydg）方法。我们证明这些策略确实保留了底层网格的结构和质量，从而降低了整体计算成本和网格复杂性。
We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of the polyhedron to be refined. This strategy is a variation of the well known Centroidal Voronoi Tessellation. The second one employs Convolutional Neural Networks to classify the "shape" of an element so that "ad-hoc" refinement criteria can be defined. This strategy can be used to enhance existing refinement strategies, including the k-means strategy, at a low online computational cost. We test the proposed algorithms considering two families of finite element methods that support arbitrarily shaped polyhedral elements, namely the Virtual Element Method (VEM) and the Polygonal Discontinuous Galerkin (PolyDG) method. We demonstrate that these strategies do preserve the structure and the quality of the underlaying grids, reducing the overall computational cost and mesh complexity.
