Compressing local atomic neighbourhood 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 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).

Leveraging genetic algorithms to maximise the predictive capabilities of the SOAP descriptor

“…Rather than adopting that approach, here we instead chose to take advantage of the compression scheme described in ref. 46. Within this scheme the SOAP power spectrum is compressed through a combination of projecting the atomic neighbour density onto the surface of the unit sphere, which reduces the radially sensitive body order, and summing over the neighbour densities of different species, which reduces the element sensitive body order.…”

“…In Table 3, we report the dimensionality as well as the accuracy of the all-all SOAP obtained with these different levels of compression and denote them using the same notation as in ref. 46; note that the μ = 0,  = 0, ν = 2 and  = 0 option corresponds to the original uncompressed SOAP vector. In light of the results reported in Table 3, we chose to apply the μ = 0,  = 1, ν = 1 and  = 0 option as it provides an excellent compromise between accuracy and compression.…”

“…It can also deal with large datasets, by leveraging the compression options recently introduced in ref. 46, and can optimise the parameters of multiple SOAP vectors at the same time.…”

DADApy: Distance-based analysis of data-manifolds in Python

“…The information imbalance proved successful in dealing with atomistic and molecular descriptors, either to directly perform compression 39 or to quantify the information loss incurred by competing compression schemes. 40 In the original article, 39 the information imbalance was also proposed for detecting causality in time series-with illustrative results shown on COVID-19 time series-and to analyze or optimize the layer representations of deep neural networks. The Base class contains basic methods of data cleaning and manipulation that are inherited in all other classes.…”

Tensor-reduced atomic density representations

“…Multiple strategies to tackle this scaling problem have been proposed including weighting [11,12] or embedding [13] the elements into a fixed dimensional space, directly reducing the element-sensitive correlation order [14] and data-driven approaches for selecting the most relevant subset or combination of the original features for a given dataset [15][16][17]. A rather different class of machine learning methods are Message Passing Neural Networks (MPNNs) [18,19].…”