Compressing local atomic neighbourhood descriptors

Abstract

AbstractMany 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 SOAP power spectrum (3-body) and the (ACE) (multiple body-orders), scales as (NS)ν where ν + 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 $${{{\mathcal{O}}}}({N}^{2}{S}^{2})$$ O ( N 2 S 2 ) to $${{{\mathcal{O}}}}\left(NS\right)$$ O N S . Secondly, we introduce a generalised 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 generalised kernel are equally applicably to any other body-ordered descriptors and we demonstrate this for the (ACSF).