Compact atomic descriptors enable accurate predictions via linear models

TL;DR

This paper demonstrates that simple linear ridge regression with a three-body local density descriptor can achieve accuracy comparable to complex machine learning models in predicting formation energies and forces, while also enabling descriptor sparsification for efficiency.

Contribution

It introduces a compact, sparse atomic descriptor that maintains high accuracy and is computationally efficient, with potential for material-agnostic applications.

Findings

Linear ridge regression performs on par with complex ML methods.

Descriptor sparsification reduces size by four times without losing accuracy.

Shared features across datasets suggest universal, optimized descriptors.

Abstract

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors.