Building machine learning force fields for nanoclusters

TL;DR

This paper evaluates Gaussian process regression for modeling interatomic forces in Ni nanoclusters, demonstrating that multi-body kernels outperform 2-body kernels and enabling efficient, accurate force field predictions for thermal stability analysis.

Contribution

It introduces a heterogeneously trained Gaussian process force field for nanoclusters, improving accuracy and versatility over traditional methods.

Findings

3- and many-body kernels predict forces with ~0.1 eV/Å error

Heterogeneous training enhances extrapolation to dissimilar structures

The developed force field accurately assesses nanocluster thermal stability

Abstract

We assess Gaussian process (GP) regression as a technique to model interatomic forces in metal nanoclusters by analysing the performance of 2-body, 3-body and many-body kernel functions on a set of 19-atom Ni cluster structures. We find that 2-body GP kernels fail to provide faithful force estimates, despite succeeding in bulk Ni systems. However, both 3- and many-body kernels predict forces within a $\sim$0.1 eV/$\text{\AA}$ average error even for small training datasets, and achieve high accuracy even on out-of-sample, high temperature, structures. While training and testing on the same structure always provides satisfactory accuracy, cross-testing on dissimilar structures leads to higher prediction errors, posing an extrapolation problem. This can be cured using heterogeneous training on databases that contain more than one structure, which results in a good trade-off between versatility and overall accuracy. Starting from a 3-body kernel trained this way, we build an efficient non-parametric 3-body force field that allows accurate prediction of structural properties at finite temperatures, following a newly developed scheme [Glielmo et al. PRB 97, 184307 (2018)]. We use this to assess the thermal stability of Ni$_{19}$ nanoclusters at a fractional cost of full ab initio calculations.