The PES is fitted by learning from the sampled data. Different representations of the coordinates, "fingerprints", or descriptors are designed. Particularly, the symmetry property can be considered in the input layer of the PIP-NN with no need to modify the NN implementation. For HD-NN, the symmetry property is retained by enforcing one identical NN to describe the energy contribution of the same chemical element. Then the exchange between like atoms does not affect the entire energy. With similar performance, the PIP-NN is faster in evaluation than the HD-NN.