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

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.

References in corpus (25)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• On representing chemical environments
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
• Machine Learning of Accurate Energy-Conserving Molecular Force Fields
• A Spectral Analysis Method for Automated Generation of Quantum-Accurate Interatomic Potentials
• Comparing molecules and solids across structural and alchemical space
• Machine Learning Unifies the Modelling of Materials and Molecules
• Machine learning prediction errors better than DFT accuracy
• Machine-learning based interatomic potential for amorphous carbon
• Nearsightedness of Electronic Matter
• How van der Waals interactions determine the unique properties of water
• How to represent crystal structures for machine learning: towards fast prediction of electronic properties
• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• Automatic Selection of Atomic Fingerprints and Reference Configurations for Machine-Learning Potentials
• Achieving DFT accuracy with a machine-learning interatomic potential: thermomechanics and defects in bcc ferromagnetic iron
• Accurate Interatomic Force Fields via Machine Learning with Covariant Kernels
• Data-driven learning of total and local energies in elemental boron
• A Machine Learning Potential for Graphene
• Growth Mechanism and Origin of High $s{p}^3$ Content in Tetrahedral Amorphous Carbon
• Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions
• Efficient nonparametric $n$-body force fields from machine learning
• Gaussian approximation potential modeling of lithium intercalation in carbon nanostructures
• Microscopic origins of the anomalous melting behaviour of high-pressure sodium

Cited by in corpus (6)

• Big-Data Science in Porous Materials: Materials Genomics and Machine Learning
• Learning the electronic density of states in condensed matter
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Unsupervised learning of representative local atomic arrangements in molecular dynamics data
• Machine learning at the atomic-scale
• Dynamically polarisable force-fields for surface simulations via multi-output classification Neural Networks