论文标题
等距转换不变和模棱两可的图形卷积网络
Isometric Transformation Invariant and Equivariant Graph Convolutional Networks
论文作者
论文摘要
图是表示对象之间成对关系的最重要数据结构之一。具体而言，嵌入在欧几里得空间中的图对于解决实际问题，例如物理模拟至关重要。将欧几里得空间中图形应用于物理模拟的关键要求是以计算有效的方式学习和推断等距转换不变和均衡的特征。在本文中，我们提出了一组基于图形卷积网络的变换不变和模型模型，称为ISOGCN。我们证明，与与几何和物理模拟数据有关的任务的最新方法相比，所提出的模型具有竞争性能。此外，所提出的模型可以扩展到具有1M顶点的图形，并比常规的有限元分析更快地进行推理，而现有的epoivariant模型无法实现。
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial requirement for applying graphs in Euclidean spaces to physical simulations is learning and inferring the isometric transformation invariant and equivariant features in a computationally efficient manner. In this paper, we propose a set of transformation invariant and equivariant models based on graph convolutional networks, called IsoGCNs. We demonstrate that the proposed model has a competitive performance compared to state-of-the-art methods on tasks related to geometrical and physical simulation data. Moreover, the proposed model can scale up to graphs with 1M vertices and conduct an inference faster than a conventional finite element analysis, which the existing equivariant models cannot achieve.
