The application of neural networks for the calibration of topological cell clusters in the ATLAS calorimeters

The principal signals of the non-compensating calorimeters employed by the ATLAS experiment at the Large Hadron Collider (LHC) are clusters of topologically connected cell signals that reconstruct three-dimensional blobs of locally deposited energy. Many of these topo-clusters provide shape and location information sensitive to the origin of the energy deposit, which can be electromagnetic or hadronic showers and shower fragments from isolated particles as well as merged full showers and shower fragments from close-by particles. A set of corresponding observables is used to apply the appropriate signal calibration to elevate the topo-cluster signal to a local hadronic energy scale. For that, the standard calibration sequence of signal classification, calibration and corrections respectively retrieves scale factors from lookup tables organised in a multi-dimensional grid spawned by this set. A new machine-learning-based technique replaces this sequential lookup with a smooth multidimensional function that is determined using two different network designs, a Deep Neural Network and a Bayesian Neural Network. The topo-cluster features serving as inputs to these networks include most of the observables used in the standard procedure, in addition to others found to be sensitive to the signal origin. The network learns the response of topo-clusters in jets found in the fully simulated final state of the the proton--proton collisions, including pile-up, and reconstructed with the ATLAS calorimeters. The result of the regression performed in this training is a prediction of this response from the employed feature set from which a local topo-cluster calibration function is derived for individual cluster. This note shows the principal feasibility of such approaches for employing such networks, which produce calibrated signals that significantly improve the linearity of the response, in particular for lower energy topo-clusters. In addition, reduced signal fluctuations lead to a significant gain of the relative energy resolution at level of individual topo-clusters over a large signal range.