WACSF - Weighted Atom-Centered Symmetry Functions as Descriptors in Machine Learning Potentials

TL;DR

This paper introduces weighted atom-centered symmetry functions (wACSFs) as efficient descriptors for machine learning potentials, offering improved generalization and reduced complexity over traditional ACSFs, with potential for automated parameter optimization.

Contribution

The paper presents wACSFs, a novel descriptor that overcomes scaling issues of ACSFs and enhances machine learning potential accuracy with fewer features.

Findings

wACSFs require fewer descriptors than ACSFs for similar resolution

wACSFs lead to better generalization in neural network potentials

Simple empirical parametrization suffices for high accuracy

Abstract

We introduce weighted atom-centered symmetry functions (wACSFs) as descriptors of a chemical system's geometry for use in the prediction of chemical properties such as enthalpies or potential energies via machine learning. The wACSFs are based on conventional atom-centered symmetry functions (ACSFs) but overcome the undesirable scaling of the latter with increasing number of different elements in a chemical system. The performance of these two descriptors is compared using them as inputs in high-dimensional neural network potentials (HDNNPs), employing the molecular structures and associated enthalpies of the 133855 molecules containing up to five different elements reported in the QM9 database as reference data. A substantially smaller number of wACSFs than ACSFs is needed to obtain a comparable spatial resolution of the molecular structures. At the same time, this smaller set of wACSFs leads to significantly better generalization performance in the machine learning potential than the large set of conventional ACSFs. Furthermore, we show that the intrinsic parameters of the descriptors can in principle be optimized with a genetic algorithm in a highly automated manner. For the wACSFs employed here, we find however that using a simple empirical parametrization scheme is sufficient in order to obtain HDNNPs with high accuracy.