Machine learning supergravity vacua

In this thesis we study maximally symmetric vacua for maximal supergravity in 4D. We will begin by showing that the structure of those vacua is determined by the gauging procedure. The consistency of the gauging, together with the extremization of the scalar potential, allows us to parameterize a system of equations that describes the vacua structure. We also examine various approaches from the literature that utilize machine learning techniques to solve these equations. In particular, we present a novel approach based on a neural network architecture that improves the efficiency of those machine learning methods. Finally, we will present an efficient algorithm for analytically solving systems of polynomial equations. This algorithm has been improved and implemented in a Python library, PyXLTensor. This library facilitates the writing, manipulation and solving of tensor expressions. Given its versatility it offers wide applicability in other fields where tensor equations need to be solved.