Potential energy surfaces (PES) are crucial to the study of reactive and nonreactive chemical systems by Monte Carlo (MC) or molecular dynamics (MD) simulations. Ideally, PES should have the accuracy provided by ab initio calculations and be set up as fast as possible. Recently, neural networks (NNs) turned out as a suitable approach for estimating PES from ab initio/DFT energy datasets. However, the accuracy of the properties determined by MC and MD simulation methods from NNs surfaces has not yet, to our knowledge, been systematically analyzed in terms of the minimum number of energy points required for training and the usage of different NN-types. The goal of this work is to train NNs for reproducing PES represented by well-known analytical potential functions, and then to assess the accuracy of the method by comparing the simulation results obtained from NNs and analytical PES. Ensembles of feed-forward neural networks (EnsFFNNs) and associative neural networks (ASNNs) are used to estimate the full energy surface. Training sets with different number of points, from 15 differently parameterized Lennard-jones (LJ) potentials, are used and argon is taken to test the network. MD simulations have been performed using the tabular potential energies, predicted by NNs, for working out thermal, structural, and dynamic properties which are compared with the values obtained from the analytical function.