The particle nature of dark matter and its role in galactic structure formation, especially at the small scales, are among the greatest outstanding questions in Lambda-CDM cosmology. Notable challenges include the core-cusp problem in dwarf galaxies and the potential discrepancies in the high-redshift galaxy abundance observed by the James Webb Space Telescope. Future surveys promise an unprecedented volume of data that will address these pressing questions in modern astrophysics. We must develop new methodologies that can efficiently interpret and connect such data to theoretical models.
In this talk, I present a multi-scale investigation into the nature of dark matter and its role in galaxy structure formation, utilizing data from astrophysical surveys, cosmological simulations, and machine learning techniques. Specifically, I focus on the recent and ongoing work in two key areas: 1) Integrating neural simulation-based inference with hydrodynamic simulations to constrain dark matter density profiles in dwarf galaxies, thereby addressing the core-cusp problem; and 2) Building an efficient theoretical framework for galaxy formation using semi-analytic models and deep generative emulators for dark matter halo merger trees. These approaches leverage machine learning's capabilities in high-dimensional data analysis and the synthetic training datasets provided by cosmological simulations, enriching our understanding of the intricate relationship between dark matter and galaxy formation.