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A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing

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. However, we find that current architectures fail to capture information from long-range correlations as effectively as domain-specific baselines, motivating future work on architectures better suited for extracting long-range information.

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