Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions

TL;DR

This paper investigates the behavior of SOAP and ACSF atomic fingerprints, revealing manifolds of quasi-constant fingerprints that hinder machine learning of four-body interactions, unlike the OM fingerprint.

Contribution

It identifies the existence of quasi-constant fingerprint manifolds in SOAP and ACSF, explaining their failure in learning four-body interactions, and contrasts this with the OM fingerprint's robustness.

Findings

Manifolds of quasi-constant SOAP and ACSF fingerprints are numerically identified.

These manifolds cause failures in machine learning four-body interactions.

OM fingerprint does not exhibit such manifolds due to its many-body nature.

Abstract

Atomic fingerprints are commonly used for the characterization of local environments of atoms in machine learning and other contexts. In this work, we study the behavior of two widely used fingerprints, namely the smooth overlap of atomic positions (SOAP) and the atom-centered symmetry functions (ACSF), under finite changes of atomic positions and demonstrate the existence of manifolds of quasi-constant fingerprints. These manifolds are found numerically by following eigenvectors of the sensitivity matrix with quasi-zero eigenvalues. The existence of such manifolds in ACSF and SOAP causes a failure to machine learn four-body interactions such as torsional energies that are part of standard force fields. No such manifolds can be found for the Overlap Matrix (OM) fingerprint due to its intrinsic many-body character.