We present a new scheme to compensate for the small-scales approximations resulting from Particle-Mesh (PM) schemes for cosmological N-body simulations. This kind of simulations are fast and low computational cost realizations of the large scale structures, but lack resolution on small scale and cannot give accurate halo matter profiles.To recover this missing accuracy, we employ a Neural network as a Fourier-space filter to parameterize the correction terms and to compensate for the PM approximations.We compare the results obtained to the ones obtained by the PGD scheme (Potential gradient descent scheme).We find that our approach outperforms PGD to the smaller scales and turns out more robust to the changes of simulation setting used during training.