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This paper studies the use of Neural Networks (NNs) for estimating the position of impinging photons in gamma ray detector modules for PET cameras based on continuous scintillators and Multi-Anode Photomultiplier Tubes (MA-PMTs). The detector under study is composed of a 49×49×10 mm3 continuous slab of LSO coupled to a flat panel H8500 MA-PMT. Four digitized signals from a charge division circuit, which collects currents from the 8×8 anode matrix of the photomultiplier, are used as inputs to the NN, thus reducing drastically the number of electronic channels required. We have simulated the computation of the position for 511 keV gamma photons impacting perpendicularly to the detector surface. Thus, we have performed a thorough analysis of the NN architecture and training procedures in order to achieve the best results in terms of spatial resolution and bias correction. Results obtained using GEANT4 simulation toolkit show a resolution of 1.3 mm/1.9 mm FWHM at the center/edge of the detector and less than 1 mm of systematic error in the position near the edges of the scintillator. The results confirm that NNs can partially model and correct the non-uniform detector response using only the position-weighted signals from a simple 2D DPC circuit. Linearity degradation for oblique incidence is also investigated. Finally, the NN can be implemented in hardware for parallel real time corrected Line-of-Response (LOR) estimation. Results on resources occupancy and throughput in FPGA are presented.