Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species

Abstract

Machine-learning potentials (MLPs) for atomistic simulations are a promising alternative to conventional classical potentials. Current approaches rely on descriptors of the local atomic environment with dimensions that increase quadratically with the number of chemical species. In this article, we demonstrate that such a scaling can be avoided in practice. We show that a mathematically simple and computationally efficient descriptor with constant complexity is sufficient to represent transition-metal oxide compositions and biomolecules containing 11 chemical species with a precision of around 3 meV/atom. This insight removes a perceived bound on the utility of MLPs and paves the way to investigate the physics of previously inaccessible materials with more than ten chemical species.

A Critical Review of Machine Learning of Energy Materials

“…Their ability to be universal function approximators makes them extremely useful for materials property predictions, if sufficient training data exist. MLPs have also been used in combination with local environment features to develop interatomic potentials . CNNs (Figure 3b) are rapidly gaining interest due to their recent feat of outperforming other ML algorithms by a considerable margin in image recognition .…”

“…c) Schematic workflow of sampling strategy combining GA and specialized NNP. At each delithiation step, GA was used to identify the most stable Li/vacancy arrangement of that composition, with specialized NNP determining the energetics of different arrangements . d) The predicted Haven ratio and e) the Arrhenius plot of Li diffusion diffusivity in α‐Li 3 N from eSNAP MD simulations .…”

“…d) The predicted Haven ratio and e) the Arrhenius plot of Li diffusion diffusivity in α‐Li 3 N from eSNAP MD simulations . Reproduced with permission . Copyright 2017 American Institute of Physics and 2018 American Institute of Physics.…”

“…The sampled structures by genetic algorithm were within the range of 100 meV per atom above the lowest energy structure for each composition, indicating its success in the determination of low‐energy metastable amorphous structures of Li x Si, which then allowed the phase diagram for amorphous Li x Si to be constructed. The same authors have also developed NNP‐type models incorporating compositional descriptors that are able to predict the energies of eleven‐species cation‐disordered lithium transition‐metal (TM) oxides LiMO 2 (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu) to within 3 meV per atom …”

Representations and descriptors unifying the study of molecular and bulk systems

“…Interested readers are referred to Reference for an overview in a chemical context. Such feature spaces can be equivalently built: From radial and spherical harmonic expansion of smoothed atomic densities via atom‐centered Gaussians, that is, the Smooth Overlap of Atomic Integrals representation, Through the arbitrary nonlinear combination of two‐ and three‐body descriptors, as in the case of Beheler‐Parrinello symmetry functions, Chebychev polynomial expansion of radial and angular distribution functions, and scaled Gaussian basis functions, or From functions of n‐body kernels …”