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Description
Ultra-high-energy cosmic rays (UHECRs) are charged particles of extraterrestrial origin reaching energies above $1\,\text{EeV}$.
Their origin and acceleration mechanisms are not understood.
Unlike in the case of gamma astronomy, UHECRs are deflected by magnetic fields.
Hence their arrival directions (AD) do not point to their sources.
The level of deflection depends on the rigidity of the particle $R\propto E/Z$, where $E$ is the energy and $Z$ the charge.
Separating light particles at ultra-high energies allows for identification of UHECR sources.
Due to the low flux of UHECRs, the direct detection of the particles is infeasible.
When a UHECR enters Earth's atmosphere, it will eventually interact with an air molecule, inducing a cascade of secondary particles, referred to as an extensive air shower (EAS).
Indirect measurements pose several challenges for estimating mass and hence charge of UHECRs.
The mass information of the UHECR is encoded in observables such as the shower depth of the shower maximum, $X_\mathrm{max}$, or the relative number of muons, $R_\mu$.
The Pierre Auger Observatory is the largest detector for measuring UHECRs in the southern hemisphere with an area of $3000\,\mathrm{km}^2$.
The Observatory comprises a surface detector array (SD) of 1660 surface detector units with a fluorescence detector (FD) of 27 optical telescopes.
The FD measures $X_\mathrm{max}$ directly, but the statistic is limited by its duty cycle of about 15\%.
The $X_\mathrm{max}$ can also be reconstructed from the signal of the EAS footprint on the ground measured by SD, with the advantage of a significant increase in statistics due to the almost continuous operation of SD.
In this contribution, we present machine learning methods for $X_\mathrm{max}$ predictions as well as their intended application in AD analyses.