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

Abstract: Extracting cosmological parameters from complex dark matter halo merger trees presents a significant challenge due to their inherent high dimensionality and intricate hierarchical structure. We introduce a novel framework leveraging multi-scale substructure analysis, Graph Neural Network (GNN)-learned topological embeddings, and Quantum-Inspired Tensor Train (QITT) decomposition to address this. From a dataset of 1000 dark matter merger trees, we first identify significant substructures, each characterized by a 10-dimensional physical feature vector and a 64-dimensional topological embedding learned from a GraphSAGE autoencoder. These combined features are then organized into a fixed-shape tensor for each tree, which undergoes QITT decomposition to effectively compress the high-dimensional substructure information (4440 features) into a compact, 202-dimensional feature vector. Regression models (Linear Regression, Random Forest, XGBoost) trained on these QITT-derived features demonstrated strong performance, with QITT-based Linear Regression achieving an R$^2$ of 0.923 for $\Omega_m$ and 0.621 for $\sigma_8$. Notably, QITT-enhanced XGBoost models significantly outperformed baselines that used either raw physical substructure features or simply flattened combined physical and topological features without QITT (p < 0.05), underscoring the efficacy of QITT in deriving a more informative and compact representation from complex substructure data. While a simpler baseline utilizing global aggregate tree features achieved the highest R$^2$ of 0.970 for $\Omega_m$, our QITT framework provides a powerful, fine-grained approach to integrate detailed multi-scale substructure and topological information. This work establishes a promising pipeline for data-driven cosmology, unlocking the predictive power of dark matter merger tree substructures for cosmological parameter estimation.

Subjects:	gr-qc; hep-th; astro-ph.CO
Cite as:	PX:2508.00074