String theory is one of the leading frameworks to study mechanisms generating exponential hierarchies in effective field theories coupled to gravity. Ultimately, such insights may allow us to shed light on open challenges in high energy physics like the cosmological constant problem. In this talk, I present novel numerical and algorithmic strategies to explicitly construct solutions of the equations of motion of string theory exhibiting such hierarchies of scales. This approach heavily relies on Machine Learning inspired tools combined with formal and software developments in string theory and algebraic geometry. After a detailed introduction to string theory compactifications, I will summarise established proposals to obtain string theory solutions with desirable features such as positive cosmological constants. Subsequently, I discuss recent computational advances that have been integral to systematically solve optimisation problems in string theory on large scales, thereby making tests of the aforementioned proposals in concrete setups feasible. I demonstrate that our methods are much more versatile and several orders of magnitude faster compared to previous approaches. In particular, I will argue that these tools enable us to address important questions concerning the statistics of string theory solutions and the resulting distributions of observables.