A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing

Julia Balla, Siddharth Mishra-Sharma, Carolina Cuesta-Lazaro, Tommi Jaakkola, Tess Smidt

Keywords: Cosmology, Point Cloud, Graph Neural Networks, Equivariance

TL;DR: We introduce an interface for benchmarking equivariant neural networks on galaxy clustering data and comparing them against non-equivariant and traditional cosmological methods.

Abstract: Efficiently processing structured point cloud data while preserving multiscale information is a key challenge across domains, from graphics to atomistic modeling. Using a curated dataset of simulated galaxy positions and properties, represented as point clouds, we benchmark the ability of graph neural networks to simultaneously capture local clustering environments and long-range correlations. Given the homogeneous and isotropic nature of the Universe, the data exhibits a high degree of symmetry. We therefore focus on evaluating the performance of Euclidean symmetry-preserving ($E(3)$-equivariant) graph neural networks, showing that they can outperform non-equivariant counterparts and domain-specific information extraction techniques in downstream performance as well as simulation-efficiency.

Submission Number: 43