Atomic energy mapping of neural network potential

We show that the intelligence of the machine-learning potential arises from its ability to infer the reference atomic-energy function from a given set of total energies. By utilizing invariant points in the feature space at which the atomic energy has a fixed reference value, we examine the atomic energy mapping of neural network potentials. Through a series of examples on Si, we demonstrate that the neural network potential is vulnerable to 'ad hoc' mapping in which the total energy appears to be trained accurately while the atomic energy mapping is incorrect in spite of its capability. We show that the energy mapping can be improved by choosing the training set carefully and monitoring the atomic energy at the invariant points during the training procedure.