The mysterious nature of Calabi-Yau metrics and hermitian Yang-Mills connections has been a persistent challenge in mathematics and theoretical physics for decades. These elusive geometric objects play a critical role in deriving semi-realistic models of particle physics from string theory. However, with no explicit expressions for them, we are left unable to compute basic quantities in top-down string models, such as particle masses and couplings. Recent breakthroughs in machine learning have opened up a new avenue for tackling this problem. In this seminar, we will explore the potential of machine learning for computing these elusive objects. Starting with a review of their relationship to effective field theories, we will then delve into the latest progress in using machine learning to calculate Calabi-Yau metrics and hermitian Yang-Mills connections numerically. Finally, we will give examples of practical applications of this new data, including a test of the so-called “swampland distance conjecture”.