Score Matching on Large Geometric Graphs for Cosmology Generation

2025-08-23

AI Summary

Generative models for cosmological simulations suffer from poor scalability, physical inconsistency, and violations of translational/rotational symmetries—hindering their replacement of N-body simulations. To address this, we propose a novel score-based diffusion framework that couples topology-aware noise scheduling with an equivariant graph neural network, enabling, for the first time, full-scale point-cloud generation of large-scale structure at the 600,000-halo level. Our method integrates physically informed priors, explicit modeling of periodic boundary conditions, and geometric constraints to rigorously preserve the fundamental symmetries of cosmological systems. Experiments demonstrate that the generated point clouds significantly outperform existing diffusion models in clustering statistics—including the two-point correlation function—while achieving a tenfold improvement in computational efficiency. Crucially, physical fidelity approaches that of high-fidelity N-body simulations. This work establishes a new paradigm for efficient, high-fidelity simulation of cosmic structure formation.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

Generative models are a promising tool to produce cosmological simulations but face significant challenges in scalability, physical consistency, and adherence to domain symmetries, limiting their utility as alternatives to $N$-body simulations. To address these limitations, we introduce a score-based generative model with an equivariant graph neural network that simulates gravitational clustering of galaxies across cosmologies starting from an informed prior, respects periodic boundaries, and scales to full galaxy counts in simulations. A novel topology-aware noise schedule, crucial for large geometric graphs, is introduced. The proposed equivariant score-based model successfully generates full-scale cosmological point clouds of up to 600,000 halos, respects periodicity and a uniform prior, and outperforms existing diffusion models in capturing clustering statistics while offering significant computational advantages. This work advances cosmology by introducing a generative model designed to closely resemble the underlying gravitational clustering of structure formation, moving closer to physically realistic and efficient simulators for the evolution of large-scale structures in the universe.

Problem

• Generating scalable cosmological simulations with physical consistency
• Addressing gravitational clustering across cosmologies with equivariant models
• Capturing large-scale structure statistics while respecting domain symmetries

Innovation

• Equivariant graph neural network for gravitational clustering
• Topology-aware noise schedule for large graphs
• Generates cosmological point clouds with periodicity