  Machine learning techniques allow a direct mapping of atomic positions and
nuclear charges to the potential energy surface with almost ab-initio accuracy
and the computational efficiency of empirical potentials. In this work we
propose a machine learning method for constructing high-dimensional potential
energy surfaces based on feed-forward neural networks. As input to the neural
network we propose an extendable invariant local molecular descriptor
constructed from geometric moments. Their formulation via pairwise distance
vectors and tensor contractions allows a very efficient implementation on
graphical processing units (GPUs). The atomic species is encoded in the
molecular descriptor, which allows the restriction to one neural network for
the training of all atomic species in the data set. We demonstrate that the
accuracy of the developed approach in representing both chemical and
configurational spaces is comparable to the one of several established machine
learning models. Due to its high accuracy and efficiency, the proposed
machine-learned potentials can be used for any further tasks, for example the
optimization of molecular geometries, the calculation of rate constants or
molecular dynamics.
