Positron Emission Tomography (PET) is among the most commonly used medical imaging modalities in clinical practice, especially for oncological applications. In contrast to conventional imaging modalities like X-ray Computed Tomography (CT) or Magnetic Resonance Imaging (MRI), PET retrieves in vivo information about biochemical processes rather than just anatomical structures. However, physical limitations and detector constraints lead to an order of magnitude lower spatial resolution in PET images. In recent years, the use of monolithic detector crystals has been investigated to overcome some of the factors limiting spatial resolution. The key to increasing PET systems' resolution is to estimate the gamma-ray interaction position in the detector as precisely as possible.In this work, we evaluate a Convolutional Neural Network (CNN) based reconstruction algorithm that predicts the gamma-ray interaction position using light patterns recorded with Silicon photomultipliers (SiPMs) on the crystal's surfaces. The algorithm is trained on data from a Monte Carlo Simulation (MCS) that models a gamma point source and a detector consisting of Lutetium-yttrium oxyorthosilicate (LYSO) crystals and SiPMs added to five surfaces. The final Mean Absolute Error (MAE) on the test dataset is 1.48 mm.