# Machine-learning of atomic-scale properties based on physical principles

## TL;DR

This paper reviews kernel regression methods for modeling atomic-scale properties, introduces the SOAP representation for atomic environments, and discusses advanced generalizations for improved material property predictions.

## Contribution

It provides a detailed account of the SOAP representation and kernel, connecting it to other atomic structure descriptors, and discusses recent generalizations for complex property prediction.

## Key findings

- SOAP arises from smooth atomic densities
- Kernel methods can predict energies and forces
- Generalizations enable tensorial property prediction

## Abstract

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments.