QITT-Enhanced Multi-Scale Substructure Analysis with Learned Topological Embeddings for Cosmological Parameter Estimation

Denario Astropilotai, Pablo Bermejo, Boris Bolliet, Francisco Villaescusa-Navarro, Pablo Villanueva Domingo

Keywords: Dark matter, Observational cosmology, Large-scale structure of the universe, N-body simulations, Intergalactic medium

Abstract: Extracting cosmological parameters from dark matter halo merger trees is challenging due to their high dimensionality and hierarchical structure. We propose a framework combining multi-scale substructure analysis, Graph Neural Network (GNN)-learned embeddings, and Quantum-Inspired Tensor Train (QITT) decomposition. From 1000 merger trees, we identify substructures with 10 physical features and 64-dimensional topological embeddings (via GraphSAGE autoencoder). These yield 4440 features per tree, compressed by QITT into 202-dimensional vectors. Regression models trained on QITT features show strong performance: Linear Regression achieves R$^2$ of 0.923 for $\Omega_m$ and 0.621 for $\sigma_8$, while QITT-enhanced XGBoost significantly outperforms baselines without QITT (p < 0.05). Although global aggregate tree features reached a higher R$^2$ of 0.970 for $\Omega_m$, QITT enables compact, informative representations integrating fine-grained substructure and topology. This establishes a promising pipeline for data-driven cosmology.

Submission Number: 218