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

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, the smooth overlap of atomic positions, Behler–Parrinello atom-centered symmetry functions, modified Behler–Parrinello symmetry functions used in the ANI-1ccx potential and the Faber–Christensen–Huang–Lilienfeld 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.

Breaking the aristotype: featurisation of polyhedral distortions in perovskite crystals

“…Furthermore, in such high dimensional methods, the features are not guaranteed to correspond directly with the displacement of atoms and thus may obstruct analyses based on conventional symmetry arguments. 84 Our approach will have an advantage in encoding polyhedral distortions in cases where the dataset size is not large enough to train general featurisation techniques. A similar discussion holds when compared with graph neural networks, where our method has an advantage in smaller datasets.…”

Fingerprint-Based Detection of Non-Local Effects in the Electronic Structure of a Simple Single Component Covalent System

“…Environment descriptors, also called atomic fingerprints, that quantify the similarity of chemical environments have recently been developed in the context of machine learning and for analysing big structural data banks [17][18][19][20]. We will use in this study mainly the fingerprints based on the eigenvalues of an atom-centered overlap matrix [21], since these descriptors have demonstrated a high reliability in detecting differences in the local environment [22]. We use a cutoff radius of 6 Å and s and p type orbitals for the overlap matrix.…”

“…In addition, we also use the SOAP fingerprint [18], which is another high resolution fingerprint [22]. For the SOAP fingerprint, we used the same cutoff radius of 6 Å together with the following parameters: n max = l max = 8, r δ = 3.0 Å and σ = 0.5 Å.…”

Ab Initio Machine Learning in Chemical Compound Space

“… 239 The overlap matrix was also included within a recent sensitivity assessment of various state-of-the art representations and performed in impressive ways. 218 A constant-size descriptor based on a combination of the CM with more common molecular graph fingerprints was also proposed in 2018. 240 …”