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

## TL;DR

This paper introduces a simplified, more efficient SOAP atomic descriptor that significantly speeds up the evaluation of machine learning interatomic potentials, maintaining accuracy and stability.

## Contribution

The authors develop a separable, analytical SOAP descriptor with recursion formulas, achieving tenfold speedups and improved stability for interatomic potential calculations.

## Key findings

- Tenfold increase in computational speed.
- Enhanced stability of radial expansion for distant neighbors.
- Maintained interpolation accuracy of GAP models.

## Abstract

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