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Title: Learning molecular energies using localized graph kernels

Abstract

We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.

Authors:
 [1];  [2]; ORCiD logo [2]
+ Show Author Affiliations
  1. Universite Paris-Est, CERMICS (ENPC) (France); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1356139
Alternate Identifier(s):
OSTI ID: 1348278
Report Number(s):
LA-UR-16-27975
Journal ID: ISSN 0021-9606
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 11; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Computer Science; Material Science

Citation Formats

Ferré, Grégoire, Haut, Terry Scot, and Barros, Kipton Marcos. Learning molecular energies using localized graph kernels. United States: N. p., 2017. Web. doi:10.1063/1.4978623.
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Ferré, Grégoire, Haut, Terry Scot, & Barros, Kipton Marcos. Learning molecular energies using localized graph kernels. United States. https://doi.org/10.1063/1.4978623
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Ferré, Grégoire, Haut, Terry Scot, and Barros, Kipton Marcos. Tue . "Learning molecular energies using localized graph kernels". United States. https://doi.org/10.1063/1.4978623. https://www.osti.gov/servlets/purl/1356139.
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@article{osti_1356139,
title = {Learning molecular energies using localized graph kernels},
author = {Ferré, Grégoire and Haut, Terry Scot and Barros, Kipton Marcos},
abstractNote = {We report that recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab initio calculations) and at speeds suitable for molecular dynamics simulation. Best performance is achieved when the known physical constraints are encoded in the machine learning models. For example, the atomic energy is invariant under global translations and rotations; it is also invariant to permutations of same-species atoms. Although simple to state, these symmetries are complicated to encode into machine learning algorithms. In this paper, we present a machine learning approach based on graph theory that naturally incorporates translation, rotation, and permutation symmetries. Specifically, we use a random walk graph kernel to measure the similarity of two adjacency matrices, each of which represents a local atomic environment. This Graph Approximated Energy (GRAPE) approach is flexible and admits many possible extensions. Finally, we benchmark a simple version of GRAPE by predicting atomization energies on a standard dataset of organic molecules.},
doi = {10.1063/1.4978623},
journal = {Journal of Chemical Physics},
number = 11,
volume = 146,
place = {United States},
year = {Tue Mar 21 00:00:00 EDT 2017},
month = {Tue Mar 21 00:00:00 EDT 2017}
}
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https://doi.org/10.1063/1.4978623
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Works referenced in this record:

Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations
journal, January 1909

  • Mercer, J.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 209, Issue 441-458
  • DOI: 10.1098/rsta.1909.0016

The Elements of Statistical Learning
book, January 2009

Multiple surface long-range interaction potentials between C ([sup 3]P[sub j]) and closed-shell molecules
journal, January 2002

  • Bettens, Ryan P. A.; Collins, Michael A.
  • The Journal of Chemical Physics, Vol. 116, Issue 1
  • DOI: 10.1063/1.1424314

Modeling cellular machinery through biological network comparison
journal, April 2006

  • Sharan, Roded; Ideker, Trey
  • Nature Biotechnology, Vol. 24, Issue 4
  • DOI: 10.1038/nbt1196

Gaussian approximation potentials: A brief tutorial introduction
journal, April 2015

  • Bartók, Albert P.; Csányi, Gábor
  • International Journal of Quantum Chemistry, Vol. 115, Issue 16
  • DOI: 10.1002/qua.24927

Representing potential energy surfaces by high-dimensional neural network potentials
journal, April 2014

Drug Discovery: A Historical Perspective
journal, March 2000

How to represent crystal structures for machine learning: Towards fast prediction of electronic properties
journal, May 2014

Permutation-invariant distance between atomic configurations
journal, September 2015

  • Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel
  • The Journal of Chemical Physics, Vol. 143, Issue 10
  • DOI: 10.1063/1.4930541

A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations
journal, February 1996

  • Ho, Tak‐San; Rabitz, Herschel
  • The Journal of Chemical Physics, Vol. 104, Issue 7
  • DOI: 10.1063/1.470984

Permutationally invariant potential energy surfaces in high dimensionality
journal, October 2009

  • Braams, Bastiaan J.; Bowman, Joel M.
  • International Reviews in Physical Chemistry, Vol. 28, Issue 4
  • DOI: 10.1080/01442350903234923

Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Nonlocality in Chemical Space
journal, June 2015

  • Hansen, Katja; Biegler, Franziska; Ramakrishnan, Raghunathan
  • The Journal of Physical Chemistry Letters, Vol. 6, Issue 12
  • DOI: 10.1021/acs.jpclett.5b00831

Two new graphs kernels in chemoinformatics
journal, November 2012

Graph Wavelet Alignment Kernels for drug Virtual Screening
journal, June 2009

  • Smalter, Aaron; Huan, Jun; Lushington, Gerald
  • Journal of Bioinformatics and Computational Biology, Vol. 07, Issue 03
  • DOI: 10.1142/s0219720009004187

Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials
journal, March 2015

Wavelets on graphs via spectral graph theory
journal, March 2011

  • Hammond, David K.; Vandergheynst, Pierre; Gribonval, Rémi
  • Applied and Computational Harmonic Analysis, Vol. 30, Issue 2
  • DOI: 10.1016/j.acha.2010.04.005

Assessment and Validation of Machine Learning Methods for Predicting Molecular Atomization Energies
journal, July 2013

  • Hansen, Katja; Montavon, Grégoire; Biegler, Franziska
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 8
  • DOI: 10.1021/ct400195d

Constructing high-dimensional neural network potentials: A tutorial review
journal, March 2015

  • Behler, Jörg
  • International Journal of Quantum Chemistry, Vol. 115, Issue 16
  • DOI: 10.1002/qua.24890

Next generation interatomic potentials for condensed systems
journal, July 2014

Graph kernels for chemical informatics
journal, October 2005

Moment Tensor Potentials: A Class of Systematically Improvable Interatomic Potentials
journal, January 2016

  • Shapeev, Alexander V.
  • Multiscale Modeling & Simulation, Vol. 14, Issue 3
  • DOI: 10.1137/15M1054183

Quantum-chemical insights from deep tensor neural networks
journal, January 2017

  • Schütt, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms13890

Ridge Regression: Biased Estimation for Nonorthogonal Problems
journal, February 1970

  • Hoerl, Arthur E.; Kennard, Robert W.
  • Technometrics, Vol. 12, Issue 1
  • DOI: 10.2307/1267351

Kernel methods in machine learning
journal, June 2008

  • Hofmann, Thomas; Schölkopf, Bernhard; Smola, Alexander J.
  • The Annals of Statistics, Vol. 36, Issue 3
  • DOI: 10.1214/009053607000000677

An Efficiently Computable Graph-Based Metric for the Classification of Small Molecules
book, January 2008

On Graph Kernels: Hardness Results and Efficient Alternatives
book, January 2003

Atom-centered symmetry functions for constructing high-dimensional neural network potentials
journal, February 2011

  • Behler, Jörg
  • The Journal of Chemical Physics, Vol. 134, Issue 7
  • DOI: 10.1063/1.3553717

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
journal, July 2015

  • Rupp, Matthias; Ramakrishnan, Raghunathan; von Lilienfeld, O. Anatole
  • The Journal of Physical Chemistry Letters, Vol. 6, Issue 16
  • DOI: 10.1021/acs.jpclett.5b01456
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    [ × clear filter / sort ]

    Works referencing / citing this record:

    ChemML : A machine learning and informatics program package for the analysis, mining, and modeling of chemical and materials data
    journal, January 2020

    • Haghighatlari, Mojtaba; Vishwakarma, Gaurav; Altarawy, Doaa
    • WIREs Computational Molecular Science, Vol. 10, Issue 4
    • DOI: 10.1002/wcms.1458

    Towards exact molecular dynamics simulations with machine-learned force fields
    journal, September 2018

    • Chmiela, Stefan; Sauceda, Huziel E.; Müller, Klaus-Robert
    • Nature Communications, Vol. 9, Issue 1
    • DOI: 10.1038/s41467-018-06169-2

    Applying machine learning techniques to predict the properties of energetic materials
    journal, June 2018

    Classification of spatially resolved molecular fingerprints for machine learning applications and development of a codebase for their implementation
    journal, January 2018

    • Reveil, Mardochee; Clancy, Paulette
    • Molecular Systems Design & Engineering, Vol. 3, Issue 3
    • DOI: 10.1039/c8me00003d

    Spherical harmonics based descriptor for neural network potentials: Structure and dynamics of Au 147 nanocluster
    journal, May 2017

    • Jindal, Shweta; Chiriki, Siva; Bulusu, Satya S.
    • The Journal of Chemical Physics, Vol. 146, Issue 20
    • DOI: 10.1063/1.4983392

    An atomistic fingerprint algorithm for learning ab initio molecular force fields
    journal, January 2018

    • Tang, Yu-Hang; Zhang, Dongkun; Karniadakis, George Em
    • The Journal of Chemical Physics, Vol. 148, Issue 3
    • DOI: 10.1063/1.5008630

    Hierarchical modeling of molecular energies using a deep neural network
    journal, June 2018

    • Lubbers, Nicholas; Smith, Justin S.; Barros, Kipton
    • The Journal of Chemical Physics, Vol. 148, Issue 24
    • DOI: 10.1063/1.5011181

    wACSF—Weighted atom-centered symmetry functions as descriptors in machine learning potentials
    journal, June 2018

    • Gastegger, M.; Schwiedrzik, L.; Bittermann, M.
    • The Journal of Chemical Physics, Vol. 148, Issue 24
    • DOI: 10.1063/1.5019667

    Prediction of atomization energy using graph kernel and active learning
    journal, January 2019

    • Tang, Yu-Hang; de Jong, Wibe A.
    • The Journal of Chemical Physics, Vol. 150, Issue 4
    • DOI: 10.1063/1.5078640

    Machine-learned electron correlation model based on correlation energy density at complete basis set limit
    journal, July 2019

    • Nudejima, Takuro; Ikabata, Yasuhiro; Seino, Junji
    • The Journal of Chemical Physics, Vol. 151, Issue 2
    • DOI: 10.1063/1.5100165

    From DFT to machine learning: recent approaches to materials science–a review
    journal, May 2019

    • Schleder, Gabriel R.; Padilha, Antonio C. M.; Acosta, Carlos Mera
    • Journal of Physics: Materials, Vol. 2, Issue 3
    • DOI: 10.1088/2515-7639/ab084b

    Efficient nonparametric n -body force fields from machine learning
    journal, May 2018

    Machine Learning a General-Purpose Interatomic Potential for Silicon
    journal, December 2018

    Machine Learning a General-Purpose Interatomic Potential for Silicon
    text, January 2018

    • Bartók, Ap; Kermode, J.; Bernstein, N.
    • Apollo - University of Cambridge Repository
    • DOI: 10.17863/cam.34909

    Applying Machine Learning Techniques to Predict the Properties of Energetic Materials
    posted_content, February 2018

    Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems.
    text, January 2018

    • Grisafi, Andrea; Wilkins, David M.; Csányi, Gábor
    • Apollo - University of Cambridge Repository
    • DOI: 10.17863/cam.34291

    Applying Machine Learning Techniques to Predict the Properties of Energetic Materials
    posted_content, February 2018

    An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields
    text, January 2017

    WACSF - Weighted Atom-Centered Symmetry Functions as Descriptors in Machine Learning Potentials
    text, January 2017

    Efficient nonparametric $n$-body force fields from machine learning
    text, January 2018

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