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We explore different ways to simplify the evaluation of the smooth overlap ofatomic positions (SOAP) many-body atomic descriptor [Bart\'{o}k et al., Phys.Rev. B 87, 184115 (2013)]. Our aim is to improve the computational efficiencyof SOAP-based similarity kernel construction. While these improved atomicdescriptors can be used for general characterization and interpolation ofatomic properties, their main target application is accelerated evaluation ofmachine-learning-based interatomic potentials within the Gaussian approximationpotential (GAP) framework [Bart\'{o}k et al., Phys. Rev. Lett. 104, 136403(2010)]. We achieve this objective by expressing the atomic densities in anapproximate separable form, which decouples the radial and angular channels. Wethen express the elements of the SOAP descriptor (i.e., the expansioncoefficients for the atomic densities) in analytical form given a particularchoice of radial basis set. Finally, we derive recursion formulas for theexpansion coefficients. This new SOAP-based descriptor allows for tenfoldspeedups compared to previous implementations, while improving the stability ofthe radial expansion for distant atomic neighbors, without degradation of theinterpolation power of GAP models.

Optimizing many-body atomic descriptors for enhanced computational performance of machine learning based interatomic potentials