Using machine learning to speed up new and upgrade detector studies: a calorimeter case

The calorimeters are an essential part of most of the existing and developing detectors in high energy physics. The high luminosity delivered by the collider causes a high multiplicity and hit occupancy in the calorimeter. In order to operate under such conditions a new generation of the calorimeters is characterised by high granularity (increased number of channels) and by the ability to measure the time of arrival of the particles to mitigate pile-up.

To obtain the planned physical performance during the R&D of modern experiments in HEP, the detailed Geant4 simulationgeant4 of the calorimeter is necessary. Such simulations are computationally expensive taking into account the large number of channels and the variety of possible options in the calorimeter module technologies, in the modules arrangement, in the reconstruction of the attributes of physical objects, etc. The optimisation cycle, within the calorimeter R&D, comprises several computationally intensive elements, such as shower development and particle transport. Processes of multi-parametric optimisation appear to be also expensive. These factors make new approaches to calorimeter development necessary. Machine learning allows a quick turnover for the optimisation cycle, when parameters are changed, and eliminates manual work for re-tuning the simulation and reconstruction.

To reconstruct the hit position of the particle reached calorimeter, we implement an approach which is based on Pythia8-generated events of $B_{s}^{0}\rightarrow J/\psi(\rightarrow\mu^{+}\mu^{-})\pi^{0}(\rightarrow\gamma\gamma)$ (hereinafter signal sample), generated with default LHCb tunings and on a data of Geant4-simulated events in the simplified high-granularity detector. This simplified simulation setup uses the same alternating layers of scintillator and lead plates (Shashlik technology), as in LHCb Electromagnetic calorimeter (ECAL)lhcbmain and it consists of a matrix of 30x30 cells of size 20.2x20.2 mm² in $\eta$ – $\phi$ plane. This allows us to emulate each type of current ECAL modules: inner, middle or outer with cells size of 40.4x40.4 mm², 60.6x60.6 mm² or 121.2x121.2 mm², respectively.

For each photon from the signal sample, we find the closest track in Geant4 simulated data.¹¹1The track affinity is based on distance in px, py, pz space. For quick nearest-neighbour lookup the 3 dimensional kd-tree was created using the package cKDTree from SciPyscipy . The calorimeter cell, in which the signal produces the hit is required to be surrounded by two layers of cells of the same type. Thus, a matrix of 5x5 cells of the same type is obtained.²²2It is assumed that the use of adjacent modules of the same type is also suitable for the borders between calorimeter regions. In this case, the adjacent module of another type on the other side of the border will be surrounded by modules of its own type. The contribution of responses of modules of different type will be compensated. We suppose that most of the clusters of the signal sample do not exceed the size of such a matrix. Inside this matrix, the cell with the highest energy deposit is searched. The barycentre of the cluster is the reconstructed position of the photon which released energy in the calorimeter. The dependence of each of the local coordinates of the signal cluster barycentre on the corresponding true coordinate of the hit position we call the S-curve due to its distinctive shape. The S-curves of both x and y coordinates for the inner region are displayed in Figure 1. The difference between the S-curve and the straight line characterises the quality of spatial reconstruction. Several approaches were tested to calibrate the S-curve (hit position reconstruction): the parametric approach and the machine learning approach using XGBoost regressorxgboost . The results of the calibration for these approaches are shown in Figure 2 and in Table 1.

As a metric of spatial resolution we use RMSE of the difference between true and reconstructed local coordinate (independent of x and y) of the hit. The observed difference in the metric, based on local coordinates x and y was found to be negligible. Therefore, all the results exploited in this metric are presented for local coordinate x.

For the parametric approach, the reconstructed local coordinate x is represented as ${a\cdot arcsinh(b\cdot x)}$. The parameters for the calibration were found using random searchrandom with 1000² points in the range (0.01, 100) for each parameter. The best parameters obtained using a parametric approach for the inner section are: a = 1.15, b = 2.07.

The selected machine learning approach was based on the extreme gradient boosting (XGBoost), and among its hyperparameters colsample_bytree, gamma, max_depth and min_child_weight were selected, which are typical for such a problem. These hyperparameters were optimised using BayesSearchCV³³3A package from scikit-optimizeskopt ., within the ranges (1, 20), (1, 10), (0.1, 0.9) and (0.3, 0.7), respectively. The chosen parameters colsample_bytree = 0.7, gamma = 0.1, max_depth = 20, min_child_weight = 10 (the set of values is for the inner section) provide best results without overtraining being observed. As a result, we used 5-fold cross-validation and trained the regressor using 30% events of the sample.

Among the requirements for the LHCb Phase 2 Upgrade ECAL, is the ability to measure the time of arrival of the photon or electron with an accuracy of few tenths of a picosecond. The difficulty is that the time-of-arrival properties are hard to reproduce in an accurate simulation. We used test beam results to evaluate important simulation parameters, as well as calibrate simulation on points measured during the test beam. The data was obtained from the electron test beam⁴⁴4Data obtained from the 30 GeV electron beam @DESY for LHCb electromagnetic calorimeter module and consists of 7848 signals, where each signal contain 1024 impulse measurements sampled with a step of 200 picoseconds (5 GHz) involving the reference time of the signal. The time of arrival has been studied in two cases: single signal and two overlapped signals. The goal of using machine learning algorithms is to evaluate limitations of the possible physics performance driven by test beam data.

The proposed approaches of spatial reconstruction and time of arrival properties of the LHCb electromagnetic calorimeter illustrate the idea of automation of the detector development and its optimisation cycle. The results obtained, using the discussed approaches, addresses physics performance aspects which are known to be computationally expensive for accurate simulation. The spatial reconstruction using both parametric and machine learning approaches was obtained. The performance of the selected XGBoost configuration surpass those of the parametric approach for each of calorimeter regions. For the pile-up mitigation, the machine learning approach demonstrates the ability to evaluate time reconstruction in the presence of the second signal.

The research leading to these results has received funding from Russian Science Foundation under grant agreement n^∘ 19-71-30020.