The high-dimensional NN (HD-NN) method, proposed by is highly scalable for large molecular systems of up to thousands of atoms. PESs have been constructed by the HD-NN method for condensed systems with diverse types of interactions from covalent bonds to metallic bonding and dispersion interactions. For HD-NN, the entire energy of the molecular system sums all energy contributions from each atom, whose local atomic chemical environment, or "fingerprint", is characterized by many-body atom-centered symmetry functions. The permutationally invariant properties are fulfilled by requiring that an identical NN (namely same NN structure with same fitting parameters) is used for the same element in the system. Atomic energy contributions are not physically meaningful, and the total electronic energies are used to obtain the optimal parameters of NNs. The HD-NN method has been adopted to represent PESs of OH + CO, H + H2S, H + NH3, H + CH4, OH + CH4, H + CH3OH. Compared to one single NN in the PIP-NN, the number of NN in the HD-NN PESs is identical to Natom. Although the resulting PESs have excellent performance, the evaluation of HD-NN is slower than PIP-NN or FI-NN.