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

Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials