Compressing local atomic neighbourhood descriptors

TL;DR

This paper presents two novel methods to compress atomic neighborhood descriptors, significantly reducing their scaling with the number of chemical elements while maintaining performance.

Contribution

The authors introduce lossless compression techniques for SOAP power spectrum and a generalized SOAP kernel that apply to various descriptors, improving scalability.

Findings

Descriptor length reduced from O(N^2 S^2) to O(NS)

Compression methods maintain comparable performance

Applicable to multiple body-ordered descriptors

Abstract

Many atomic descriptors are currently limited by their unfavourable scaling with the number of chemical elements $S$ e.g. the length of body-ordered descriptors, such as the Smooth Overlap of Atomic Positions (SOAP) power spectrum (3-body) and the Atomic Cluster Expansion (ACE) (multiple body-orders), scales as $(NS)^\nu$ where $\nu+1$ is the body-order and $N$ is the number of radial basis functions used in the density expansion. We introduce two distinct approaches which can be used to overcome this scaling for the SOAP power spectrum. Firstly, we show that the power spectrum is amenable to lossless compression with respect to both $S$ and $N$, so that the descriptor length can be reduced from $\mathcal{O}(N^2S^2)$ to $\mathcal{O}\left(NS\right)$. Secondly, we introduce a generalized SOAP kernel, where compression is achieved through the use of the total, element agnostic density, in combination with radial projection. The ideas used in the generalized kernel are equally applicably to any other body-ordered descriptors and we demonstrate this for the Atom Centered Symmetry Functions (ACSF). Finally, both compression approaches are shown to offer comparable performance to the original descriptor across a variety of numerical tests.