Atomic-Scale Representation and Statistical Learning of Tensorial Properties

@article{Grisafi2019AtomicScaleRA,
  title={Atomic-Scale Representation and Statistical Learning of Tensorial Properties},
  author={Andrea Grisafi and David M. Wilkins and Michael J. Willatt and M. Ceriotti},
  journal={ACS Symposium Series},
  year={2019}
}
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general… 
8 Citations

Figures from this paper

Physics-Inspired Structural Representations for Molecules and Materials.

This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models.

General Atomic Neighborhood Fingerprint for Machine Learning-Based Methods

This work presents a general, simple, and elegant fingerprint that can be used to learn different electronic/atomistic/structural properties, irrespective of their scalar, vector, or tensorial nature.

E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials

The NequIP method achieves state-of-the-art accuracy on a challenging and diverse set of molecules and materials while exhibiting remarkable data efficiency, challenging the widely held belief that deep neural networks require massive training sets.

Insights into Non-Covalent Interactions with a Machine-Learned Electron Density

A transferable and scalable machine-learning model capable of predicting the total electron density directly from the atomic coordinates is presented, used to access qualitative and quantitative insights beyond the underlying rho(r) in a diverse ensemble of sidechain-sidechain dimers extracted from the BioFragment database.

Prediction of Energetic Material Properties from Electronic Structure Using 3D Convolutional Neural Networks

We develop a convolutional neural network capable of directly parsing the 3D electronic structure of a molecule described by spatial point data for charge density and electrostatic potential

Atomic cluster expansion of scalar, vectorial, and tensorial properties including magnetism and charge transfer

The atomic cluster expansion (Drautz, Phys. Rev. B 99, 014104 (2019)) is extended in two ways, the modelling of vectorial and tensorial atomic properties and the inclusion of atomic degrees of

Efficient Quantum Vibrational Spectroscopy of Water with High-Order Path Integrals: From Bulk to Interfaces.

This work shows that the large cost of calculating the quantum vibrational spectra of aqueous systems can be dramatically reduced compared with standard path integral methods by using approximate quantum dynamics based on high-order path integrals.

Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning

A clustering/regression/classification implementation of MOB-ML is introduced, which is found to recapitulate chemically intuitive groupings of the frontier molecular orbitals, and the combined RC/LR/RFC and RC/GPR/RFC implementations are found to provide good prediction accuracy with greatly reduced wall-clock training times.

References

SHOWING 1-10 OF 39 REFERENCES

Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems.

This work introduces a formalism that extends existing schemes and makes it possible to perform machine learning of tensorial properties of arbitrary rank, and for general molecular geometries, and derives a tensor kernel adapted to rotational symmetry.

Atom-density representations for machine learning.

An abstract definition of chemical environments that is based on a smoothed atomic density is introduced, using a bra-ket notation to emphasize basis set independence and to highlight the connections with some popular choices of representations for describing atomic systems.

Machine learning unifies the modeling of materials and molecules

A machine-learning model, based on a local description of chemical environments and Bayesian statistical learning, provides a unified framework to predict atomic-scale properties and captures the quantum mechanical effects governing the complex surface reconstructions of silicon.

Feature optimization for atomistic machine learning yields a data-driven construction of the periodic table of the elements.

This work shows how one can generalize the SOAP kernel to introduce a distance-dependent weight that accounts for the multi-scale nature of the interactions, and a description of correlations between chemical species, to improve substantially the performance of ML models of molecular and materials stability.

Generalized neural-network representation of high-dimensional potential-energy surfaces.

A new kind of neural-network representation of DFT potential-energy surfaces is introduced, which provides the energy and forces as a function of all atomic positions in systems of arbitrary size and is several orders of magnitude faster than DFT.

Transferable Machine-Learning Model of the Electron Density

An atom-centered, symmetry-adapted framework is introduced to machine-learn the valence charge density based on a small number of reference calculations, which can be used to interpret experiments, accelerate electronic structure calculations, and compute electrostatic interactions in molecules and condensed-phase systems.

On representing chemical environments

It is demonstrated that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighborhood density function.

Non-covalent interactions across organic and biological subsets of chemical space: Physics-based potentials parametrized from machine learning.

A combination of physics-based potentials with machine learning (ML) is proposed, coined IPML, which is transferable across small neutral organic and biologically relevant molecules and able to handle new molecules and conformations without explicit prior parametrization.

Accurate molecular polarizabilities with coupled cluster theory and machine learning

Using a symmetry-adapted machine-learning approach, it is demonstrated that it is possible to predict the LR-CCSD molecular polarizabilities of these small molecules with an error that is an order of magnitude smaller than that of hybrid density functional theory (DFT) at a negligible computational cost.

Machine learning of molecular electronic properties in chemical compound space

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful,