Fast Training Data Generation for Machine Learning Analysis of Cosmic Ray Showers

Applying Machine Learning (ML) methods for the analysis of muon lateral distributions in Extensive Air Showers detected by citizen science projects, while taking into account the spatial distribution of detectors requires enormous training data sets. Therefore, generating these data sets with typical Monte Carlo (MC) generators like CORSIKA is computationally prohibitive. Here we present a method which by the application of special augmentation procedures produces the training dataset that is compatible in all essential aspects to the data produced with regular MC computations while avoiding their time overhead. We utilize the Nakamura-Kamata-Greisen (NKG) distribution which was proven to be an attractive alternative to full-fledged simulations. The simulation of $10^{4}$ muons at the ground level takes just a few seconds using our implementation of the NKG approach. For $10^{6}$ muons this figure is still around 1 minute. For comparison, CORSIKA based simulation performed on Prometheus supercomputer at CYFRONET computing center an ensemble of $\sim 100$ showers initiated by a particle of $10^{16} eV$ resulted in $\sim 10^{4}$ muons and $\sim 10^{5}$ electrons required computation time of the order of a few days.