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 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 \({{{\mathcal{O}}}}({N}^{2}{S}^{2})\) to \({{{\mathcal{O}}}}\left(NS\right)\). 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).

许多原子描述符目前受到其与化学元素数量S的不利缩放比例的限制，例如，主体有序描述符的长度，例如 SOAP 功率谱（3-主体）和 (ACE)（多个主体顺序），标度作为 ( N S ) ^ν其中ν  + 1 是体阶，N是用于密度扩展的径向基函数的数量。我们介绍了两种不同的方法，可用于克服 SOAP 功率谱的这种缩放问题。首先，我们证明了功率谱对于S和N都适用于无损压缩，因此描述符长度可以从\({{{\mathcal{O}}}}({N}^{2}{S}^{2})\)到\({{{\mathcal{O}}}}\left(NS\对）\）。其次，我们引入了一个通用的 SOAP 内核，其中通过使用与元素无关的总密度与径向投影相结合来实现压缩。广义内核中使用的想法同样适用于任何其他体序描述符，我们为 (ACSF) 演示了这一点。