An assessment of the structural resolution of various fingerprints commonly used in machine learning

TL;DR

This paper compares various atomic environment fingerprints used in computational materials science, analyzing their ability to distinguish local atomic environments and their invariance to atomic movements, with implications for machine learning applications.

Contribution

It provides a comprehensive comparison of multiple fingerprint methods, introducing a sensitivity matrix to quantify invariance and analyzing correlations with physical quantities.

Findings

Overlap Matrix (OM) and SOAP show high resolution of local environments.

Certain atomic movements leave some fingerprints nearly invariant.

Fingerprint variations correlate with physical quantities like forces.

Abstract

Atomic environment fingerprints are widely used in computational materials science, from machine learning potentials to the quantification of similarities between atomic configurations. Many approaches to the construction of such fingerprints, also called structural descriptors, have been proposed. In this work, we compare the performance of fingerprints based on the Overlap Matrix(OM), the Smooth Overlap of Atomic Positions (SOAP), Behler-Parrinello atom-centered symmetry functions (ACSF), modified Behler-Parrinello symmetry functions (MBSF) used in the ANI-1ccx potential and the Faber-Christensen-Huang-Lilienfeld (FCHL) fingerprint under various aspects. We study their ability to resolve differences in local environments and in particular examine whether there are certain atomic movements that leave the fingerprints exactly or nearly invariant. For this purpose, we introduce a sensitivity matrix whose eigenvalues quantify the effect of atomic displacement modes on the fingerprint. Further, we check whether these displacements correlate with the variation of localized physical quantities such as forces. Finally, we extend our examination to the correlation between molecular fingerprints obtained from the atomic fingerprints and global quantities of entire molecules.