Sensitivity and Dimensionality of Atomic Environment Representations used for Machine Learning Interatomic Potentials

TL;DR

This paper systematically classifies atomic environment representations used in machine learning interatomic potentials, analyzing their sensitivity to perturbations and effective dimensionality across various datasets, revealing stability issues and opportunities for compression.

Contribution

It provides a comprehensive classification and analysis of atomic environment representations, highlighting stability concerns and demonstrating significant potential for dimensionality reduction and improved model accuracy.

Findings

None of the representations are linearly stable under tangential perturbations.

Some representations, like CHSF, have instabilities that can be fixed with redefinition.

Most representations can be compressed without losing accuracy.

Abstract

Faithfully representing chemical environments is essential for describing materials and molecules with machine learning approaches. Here, we present a systematic classification of these representations and then investigate: (i) the sensitivity to perturbations and (ii) the effective dimensionality of a variety of atomic environment representations, and over a range of material datasets. Representations investigated include Atom Centred Symmetry Functions, Chebyshev Polynomial Symmetry Functions (CHSF), Smooth Overlap of Atomic Positions, Many-body Tensor Representation and Atomic Cluster Expansion. In area (i), we show that none of the atomic environment representations are linearly stable under tangential perturbations, and that for CHSF there are instabilities for particular choices of perturbation, which we show can be removed with a slight redefinition of the representation. In area (ii), we find that most representations can be compressed significantly without loss of precision, and further that selecting optimal subsets of a representation method improves the accuracy of regression models built for a given dataset.