In searching for new physics beyond the Standard Model at the Large Hadron Collider one of the most important ingredients is accurate knowledge of the cross section for the production of the new particles. In quantum field theory this can be calculated as a series expansion in the coupling (of the strong force), where complications in evaluating the terms grow unreasonably beyond the first term. Results are (usually) know for the second term, however, in the form of computationally challenging integrals that must be re-evaluated for every value of the parameters of the new physics model. Typically, an evaluation of all relevant cross sections for a given parameter point in a model would take on the scale of hours. This makes investigations of the parameter space brutal in terms of the necessary computing power.
We have an ongoing long term project where we use a multi-prong attack of modern computational methods, programming on GPUs, improving existing results from quantum field theory, and some methods from machine learning (Gaussian processes and Bayesian neural networks), to speed up high precision calculations of cross sections on High Performance Computers (HPC). The goal is to allow fast evaluation of the cross sections -- typically within one second -- and a reliable estimate of the associated error. An example of code developed in this project can be found here: github.com/jeriek/xsec.
We can offer a number of master thesis projects with different focus within this general topic, covering all sorts of tasks from higher order quantum field theory calculations of cross sections to improve precision, via hard core C++ coding projects for computational speed, to pure machine learning projects performing fast regression on existing cross section samples, and anything in between.