During the “Run 3” period of operation of the Large Hadron Collider LHC, the acquisition of data is gigantic. For accurate measurements, a complex computer reconstruction of the collision events is required, where the reconstruction of particle tracks is one of the biggest challenges. In addition to the accuracy of the track reconstruction procedures, the speed of the algorithms is also essential, as this limits the amount of data that can be captured. The use of machine learning methods and the implementation of new methods on modern computer architectures (GPU - graphical processing unit) show great promise in upgrading existing track reconstruction procedures. The development of such algorithms requires an understanding of the physical background of the problem, from the interaction of particles with matter
in the detector to the understanding of the kinematics of the physical processes, as predicted by the Standard Model and possible new physics processes. The success of the procedures must also be checked based on the existing data collected at the
LHC. The goal of the master thesis is to find and develop alternative extrapolation methods for the accurate reconstruction of charged particle tracks in the magnetic field. For this purpose, we present three methods based on functional predictions
of state vectors, with which we avoid the slow adaptive numerical integration. The first method is called the parametrized extrapolator and it works as a perturbative expansion around ideal tracks, which come exactly from the origin. The second
method is based on a multi-dimensional functional ansatz whose parameters we fit by minimizing the χ^2 on a large dataset by using SVD. The last is the GPR method, which fits correlations between sparse measurements, by which it then constructs a probability distribution around the most probable outcome. In the end, we implement and test all three methods and check that they are able to replicate the required accuracy.
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