Machine learning high multiplicity matrix elements for electron-positron and hadron-hadron colliders

The LHC is a large-scale particle collider experiment collecting vast quantities of experimental data to study the fundamental particles, and forces, of nature. Theoretical predictions made with the SM can be compared with observables measured at experiments. These predictions rely on the use of Monte Carlo event generators to simulate events which demand the evaluation of a matrix element. For high multiplicity processes this can take up a significant portion of the time spent simulating an event. In this thesis, we explore the usage of machine learning to accelerate the evaluation of matrix elements by introducing a factorisation-aware neural network model. Matrix elements are plagued with singular structures in regions of phase-space where particles become soft or collinear, however, the behaviour of the matrix element in these limits is well-understood. By exploiting the factorisation property of matrix elements in these limits, the model can learn how to best represent the approximation of the matrix elements as a linear combination of singular functions. We examine the application of the model to e−e+ annihilation matrix elements at tree-level and one-loop level, as well as to leading order pp collisions where the acceleration of event generation is critical for current experiments.