Deep learning based event reconstruction for the Limadou High-Energy Particle Detector

Deep learning algorithms have gained importance in particle physics in the last few years. They have been shown to outperform traditional strategies in particle identification, tracking and energy reconstruction in the most modern high-energy physics experiments. The attractive feature of these techniques is their ability to model large dimensionality inputs and catch nontrivial correlations among the variables, which could be hidden or not easy to model. This paper focuses on the application of deep neural networks to the event reconstruction of the Limadou High-Energy Particle Detector on board the China Seismo-Electromagnetic Satellite. The core of the reconstruction chain is a set of fully connected neural networks that reconstructs the nature, the arrival direction and the kinetic energy of incoming electrons and protons, starting from the signals recorded in the detector. These networks are trained on a dedicated Monte Carlo simulation as representative as possible of real data. We describe the simulation, architecture and methodology adopted to design and train the networks, and finally report on the performance measured on simulated and flight data.

Figure 1

Limadou HEPD CAD rendering.

Figure 2

Event display of a nearly-vertical 200 MeV proton. Sensitive volumes are overlaid in blue, support structures and auxiliary volumes in gray. The red track represents the primary proton, while the white square on top is the generation point. The points represent the energy deposits from particles to materials. Colors represent the amount deposited energy: white corresponds to $\sim 0.1\mathrm{MeV}$, green to $\sim 1\mathrm{MeV}$, and purple to $\sim 100\mathrm{MeV}$.

Figure 3

Normalized distribution of energy (a) and polar angle $\theta$ (b) for simulated electrons are shown in dotted black. The solid black distribution represents events traversing the trigger and the first two calorimeter planes without hitting the lateral veto. The distributions are similar for protons.

Figure 4

Signal profiles for the simulation of an electron (a) and a proton (b). In the latter case the Bragg peak in the 14th-15th planes is clearly visible. The vertical axis reports the sum of ADC counts from the pair of PMTs coupled to each scintillating tile.

Figure 5

Correlation matrices between input and target variables for simulated electrons (a) and protons (b). The color scale represents the linear correlation coefficient between variables.

Figure 6

Validation losses for ${\mathrm{FCNN}}_{\mathrm{pid}}$ (a), ${\mathrm{FCNN}}_{\mathrm{kin}}$ for electrons (b) and ${\mathrm{FCNN}}_{\mathrm{kin}}$ for protons (c), represented for training and validation as a function of training epoch.

Figure 7

DL-based particle identification efficiency as a function of the kinetic energy of primary electrons (red triangles) and protons (black squares). Error bars represent statistical uncertainty.

Figure 8

Predicted versus true position for protons after preselection (1). The color scale specifies the number of events per bin. The red line is the bisector.

Figure 9

Energy predicted by the DL-based algorithms as a function of true energy for protons (a) and electrons (b). The color scale represents the number of events in each bin. The red line is the bisector.

Figure 10

Energy resolution of ${\mathrm{FCNN}}_{\mathrm{kin}}$ as a function of the predicted energy for electrons (a) and protons (b). Error bars represents the statistical uncertainty. See the text for details.

Figure 11

Angular difference $\mathrm{\Psi }$ between the predicted arrival direction and the true one is shown for protons (a) and electrons (b).

Figure 12

Kinetic energy (a) and arrival direction (b) predictions from ${\mathrm{FCNN}}_{\mathrm{kin}}$ for beamed electrons ($E_{\mathrm{beam}}=60\mathrm{MeV}$ and $(\theta ,\varphi )=(0°,0°)$). The color scale specifies the number of events.

Figure 13

Kinetic energy and arrival direction predictions from ${\mathrm{FCNN}}_{\mathrm{kin}}$ for beamed protons. In plots (a) and (b) protons have $E_{\mathrm{beam}}=154\mathrm{MeV}$ and $(\theta ,\varphi )=(0°,0°)$). In plots (c) and (d) protons have $E_{\mathrm{beam}}=70\mathrm{MeV}$ and $(\theta ,\varphi )=(15°,270°)$. The color scale specifies the number of events.

Figure 14

Distribution of reconstructed energy for protons (a) and electrons (b). Monte Carlo events (red triangles) are reweighted as described in the text. Error bars represent statistical uncertainty.

Figure 15

Distribution of reconstructed polar angle $\theta$ for protons (a) and electrons (b). Monte Carlo events (red triangles) are reweighted as described in the text. Error bars represent statistical uncertainty.