Machine learning applications to energy reconstruction of gamma-ray showers for the Tibet AS\(\gamma \) experiment

Abstract

In order to improve the energy reconstruction accuracy of gamma-ray events observed by ground-based array experiments, this work propose a new energy estimator based on machine learning (ML) algorithm to determine the energies of gamma ray induced air showers in the energy range between 1 TeV and 10 PeV. We carry out a full Monte Carlo (MC) simulation using the Tibet air shower array and underground muon detector array, located at an altitude of 4,300 m above sea level. The MC simulated gamma-ray data are used to extract characteristic parameters depicting the air shower information, which are then fed into the ML model for training on both high-energy data sets (\(E >\sim 10\) TeV) and low-energy data sets (\(E < 10\) TeV). In our simulation data tests, we found that the ML method showed significant advantages over traditional energy estimators (S50, \(N_e\), and \(\sum \rho \)), with improved energy resolution for both low and high energy datasets. Compared to the traditional estimator, the energy resolution improves by approximately 30% for the inner array events and 55% for the outer array events at \(E < 10\) TeV. At around 100 TeV, the energy resolution for large zenith angle events in the outer array improves by approximately 20%. This work also found that while the energy resolution of events falling the inside array can only be slightly improved, however, events outside array and at large zenith shower clear improvements. Moreover, it is particularly noteworthy that the ML method has little difference in the energy resolution of the inner and outer array events. The enhanced energy resolution achieved through the machine learning method for outer array events reduces the limitations imposed by the observation area, resulting in an approximately 30% improvement in statistical events. This method is suitable for ground-based array experiments in gamma-ray astronomy, and provides some technical support for further study of the primary gamma-ray energy reconstruction.