  Machine learning of atomic-scale properties is revolutionizing molecular
modelling, making it possible to evaluate inter-atomic potentials with
first-principles accuracy, at a fraction of the costs. The accuracy, speed and
reliability of machine-learning potentials, however, depends strongly on the
way atomic configurations are represented, i.e. the choice of descriptors used
as input for the machine learning method. The raw Cartesian coordinates are
typically transformed in "fingerprints", or "symmetry functions", that are
designed to encode, in addition to the structure, important properties of the
potential-energy surface like its invariances with respect to rotation,
translation and permutation of like atoms. Here we discuss automatic protocols
to select a number of fingerprints out of a large pool of candidates, based on
the correlations that are intrinsic to the training data. This procedure can
greatly simplify the construction of neural network potentials that strike the
best balance between accuracy and computational efficiency, and has the
potential to accelerate by orders of magnitude the evaluation of Gaussian
Approximation Potentials based on the Smooth Overlap of Atomic Positions
kernel. We present applications to the construction of neural network
potentials for water and for an Al-Mg-Si alloy, and to the prediction of the
formation energies of small organic molecules using Gaussian process
regression.
