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Title: Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors

Abstract

Here, we explore the potential of a data-driven approach to the design of exchange-correlation (xc) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small molecules containing C, H, O, and N along with a neural network regression model. The machine learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce the exchange-correlation portion of B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 Å. Themore » findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine learning regression models is a promising framework for xc functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.« less

Authors:
 [1];  [1]
  1. Georgia Inst. of Technology, Atlanta, GA (United States)
Publication Date:
Research Org.:
Georgia Inst. of Technology, Atlanta, GA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1593730
Alternate Identifier(s):
OSTI ID: 1546404
Grant/Contract Number:  
SC0019410
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Materials
Additional Journal Information:
Journal Volume: 3; Journal Issue: 6; Journal ID: ISSN 2475-9953
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 36 MATERIALS SCIENCE; machine learning; exchange correlation; rotational invariance

Citation Formats

Lei, Xiangyun, and Medford, Andrew J. Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors. United States: N. p., 2019. Web. doi:10.1103/PhysRevMaterials.3.063801.
Lei, Xiangyun, & Medford, Andrew J. Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors. United States. doi:10.1103/PhysRevMaterials.3.063801.
Lei, Xiangyun, and Medford, Andrew J. Wed . "Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors". United States. doi:10.1103/PhysRevMaterials.3.063801.
@article{osti_1593730,
title = {Design and analysis of machine learning exchange-correlation functionals via rotationally invariant convolutional descriptors},
author = {Lei, Xiangyun and Medford, Andrew J.},
abstractNote = {Here, we explore the potential of a data-driven approach to the design of exchange-correlation (xc) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small molecules containing C, H, O, and N along with a neural network regression model. The machine learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce the exchange-correlation portion of B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 Å. The findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine learning regression models is a promising framework for xc functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.},
doi = {10.1103/PhysRevMaterials.3.063801},
journal = {Physical Review Materials},
number = 6,
volume = 3,
place = {United States},
year = {2019},
month = {6}
}

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