A Systematic Review of Mathematical reconstruction of dark matter density profiles in galaxies: Methods, Architectures, and Future Research Directions

Abstract

The reconstruction of dark matter density profiles in galaxies remains one of the most fundamental challenges in modern astrophysics, directly impacting our understanding of galactic dynamics, structure formation, and cosmology. Despite extensive observational evidence supporting the existence of dark matter, its precise distribution within galaxies continues to be inferred indirectly through mathematical modeling and inversion techniques applied to observational data such as rotation curves, gravitational lensing, and stellar kinematics. This paper presents a systematic review of mathematical reconstruction methods for dark matter density profiles, focusing on recent advances in analytical, numerical, and machine learning–driven approaches. The study examines parametric models such as Navarro–Frenk–White and Einasto profiles, non-parametric inversion techniques, Bayesian inference frameworks, and emerging deep learning architectures designed to reconstruct density distributions from sparse or noisy data. Key findings highlight the growing integration of hybrid methods combining physics-based modeling with data-driven optimization, significantly improving reconstruction accuracy and robustness. The review identifies critical challenges, including degeneracy in solutions, observational uncertainties, and scalability of models. Contributions of this work include a structured synthesis of recent literature, identification of methodological trends, and a forward-looking perspective on integrating artificial intelligence and high-performance computing in dark matter modeling.