Local invertibility and sensitivity of atomic structure-feature mappings.

ABSTRACT: Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety of representations that can be used to convert them into a finite set of symmetric descriptors or features. Methods: Here, we analyze the sensitivity of the mapping to atomic displacements, using a singular value decomposition of the Jacobian of the transformation to quantify the sensitivity for different configurations, choice of representations and implementation details.  Results: We show that the combination of symmetry and smoothness leads to mappings that have singular points at which the Jacobian h

SUBMITTER: Pozdnyakov SN 

PROVIDER: S-EPMC10445828 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature