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

WACSF - Weighted Atom-Centered Symmetry Functions as Descriptors in Machine Learning Potentials