In this numerical study, we propose a fiber distributed curvature sensor based on the analysis of the spectral transmission of a long period fiber grating (LPG) with a neural network. A simulation of the optical transmissions of a proposed 6-cm LPG structure for different curvature profiles is first performed using EigenMode Expansion and a coupled-mode theory algorithm. Both fiber curvature profiles and their corresponding optical transmission spectra are then injected into a four dense layer neural network which, after training, leads to a 0.40% relative median estimation error in the bending profiles. This paper demonstrates the efficiency of neural network-based optical sensors to analyze non-uniform perturbations, while also revealing long-period gratings to be promising candidates for such systems.