  We introduce weighted atom-centered symmetry functions (wACSFs) as
descriptors of a chemical system's geometry for use in the prediction of
chemical properties such as enthalpies or potential energies via machine
learning. The wACSFs are based on conventional atom-centered symmetry functions
(ACSFs) but overcome the undesirable scaling of the latter with increasing
number of different elements in a chemical system. The performance of these two
descriptors is compared using them as inputs in high-dimensional neural network
potentials (HDNNPs), employing the molecular structures and associated
enthalpies of the 133855 molecules containing up to five different elements
reported in the QM9 database as reference data. A substantially smaller number
of wACSFs than ACSFs is needed to obtain a comparable spatial resolution of the
molecular structures. At the same time, this smaller set of wACSFs leads to
significantly better generalization performance in the machine learning
potential than the large set of conventional ACSFs. Furthermore, we show that
the intrinsic parameters of the descriptors can in principle be optimized with
a genetic algorithm in a highly automated manner. For the wACSFs employed here,
we find however that using a simple empirical parametrization scheme is
sufficient in order to obtain HDNNPs with high accuracy.
