Advancing Particle Physics with Sophisticated Computational Frameworks

The Standard Model (SM) of particle physics is one of the most complete mathematical models of physical phenomena to date. Even so, it cannot explain experimental results like the existence of particle dark matter and the fact that neutrino masses are non-zero. Explaining such results will necessitate developing a beyond the SM (BSM) theoretical description of particle physics. What form this BSM physics will take has become increasingly unclear; many elegant theories which were expected to appear in recent experiments have not emerged. Thus, we find ourselves at a cross-roads, in need of new perspectives and new computational frameworks to push our theoretical description of physics forward.New perspectives will come from challenging previously-held assumptions in the pursuit of fundamentally new descriptions, but challenging such assumptions often presents practical computational challenges. Therefore, these new perspectives must also be accompanied by new computational frameworks. Computational frameworks can come in many forms, from the purely mathematical to the largely numerical. In particular, in recent years machine learning (ML) has become an increasingly accessible and powerful computational tool for scientific applications. Crafting novel BSM theories will require us to investigate and embrace the full spectrum of computational frameworks. Additionally, one of the best ways to spark new insights is to closely collaborate with and draw inspiration from other fields, such as mathematics and computer science.In this thesis, we present two examples of how advanced computational frameworks can be used to aid in investigating new physics perspectives. In one example, we see how the purely mathematical framework of optimal transport (OT) theory can be used in tandem with advanced ML methods to enable a new perspective on particle physics simulations. The result is a novel strategy which lays the foundations for a completely data-driven, end-to-end simulation of particle collisions at the Large Hadron Collider. In a second example, we see work which considers a new perspective on what the history of our universe might have looked like. In particular, we consider how the abundance of a WIMP dark matter candidate could be altered by considering a phase of electroweak force confinement early in the universe. Considering this model while making relatively few assumptions was aided by the application of advanced numerical computational tools.We begin with both high-level and technical background on the topics relevant to these works. We conclude by discussing future directions for these works, as well as briefly giving general thoughts on strategies for applying the computational framework of ML to problems in theoretical particle physics more broadly