Cosmology with Topological Deep Learning

Jun-Young Lee

doi:doi:10.3847/1538-4357/ade806

2025-08-04

PRE

Jun-Young Lee

Francisco Villaescusa-Navarro

DOI：doi:10.3847/1538-4357/ade806

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摘要

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标准宇宙学模型中的冷暗物质假定了结构的层次化形成。我们引入拓扑神经网络（TNNs），将其实现为在更高阶结构上的消息传递神经网络，以有效捕获这些层次中固有的拓扑信息，而传统的图神经网络（GNNs）无法对此进行建模。我们的方法不仅考虑构成图的顶点和边，还扩展到更高阶的单元，如四面体、簇和超边。这使得不同结构间的消息传递可以在组合复形内进行。此外，我们的TNNs被设计为保持E(3)不变性，这指的是源于平移、反射和旋转不变性的对称性。当应用于Quijote套件时，我们的TNNs实现了均方误差的显著降低。与缺乏更高阶消息传递的GNNs相比，ClusterTNNs在Ωm和σ8上分别实现了最高22%和34%的改进，而最佳的FullTNN在σ8上实现了最高60%的改进。在CAMELS套件的背景下，我们的模型产生了与当前GNN基准相当的结果，尽管性能略有下降。我们强调，我们的拓扑和对称感知神经网络在建模宇宙的大尺度结构方面提供了更强的表达能力。

Keyword:

topological neural networks

hierarchical structure formation

E(3) invariance

message-passing

large-scale structure

期刊

Astrophysical Journal

IF:

5.4

论文数:

8.3W

被引数:

32.0W

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