Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant way using only topological and geometric information. Our approach is based on creating and analyzing sufficient statistics and uses a graph neural network. We demonstrate the effectiveness of our approach using a synthetic mesh data set.

翻译：分析嵌入单纯复形（如三角形网格和图）是许多领域中的重要问题。我们提出了一种新方法，仅利用拓扑和几何信息，以细分不变和等距不变的方式分析嵌入单纯复形。该方法基于创建和分析充分统计量，并采用图神经网络。我们通过一个合成网格数据集展示了该方法的有效性。