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:
-
- Universite Paris-Est, CERMICS (ENPC) (France); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- 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.
Ferré, Grégoire, Haut, Terry Scot, & Barros, Kipton Marcos. Learning molecular energies using localized graph kernels. United States. https://doi.org/10.1063/1.4978623
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.
@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}
}
Web of Science
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
The Elements of Statistical Learning
book, January 2009
- Hastie, Trevor; Tibshirani, Robert; Friedman, Jerome
- Springer Series in Statistics
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
Modeling cellular machinery through biological network comparison
journal, April 2006
- Sharan, Roded; Ideker, Trey
- Nature Biotechnology, Vol. 24, Issue 4
Gaussian approximation potentials: A brief tutorial introduction
journal, April 2015
- Bartók, Albert P.; Csányi, Gábor
- International Journal of Quantum Chemistry, Vol. 115, Issue 16
Representing potential energy surfaces by high-dimensional neural network potentials
journal, April 2014
- Behler, J.
- Journal of Physics: Condensed Matter, Vol. 26, Issue 18
Drug Discovery: A Historical Perspective
journal, March 2000
- Drews, J.
- Science, Vol. 287, Issue 5460
How to represent crystal structures for machine learning: Towards fast prediction of electronic properties
journal, May 2014
- Schütt, K. T.; Glawe, H.; Brockherde, F.
- Physical Review B, Vol. 89, Issue 20
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
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
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
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
Two new graphs kernels in chemoinformatics
journal, November 2012
- Gaüzère, Benoit; Brun, Luc; Villemin, Didier
- Pattern Recognition Letters, Vol. 33, Issue 15
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
Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials
journal, March 2015
- Thompson, A. P.; Swiler, L. P.; Trott, C. R.
- Journal of Computational Physics, Vol. 285
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
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
Constructing high-dimensional neural network potentials: A tutorial review
journal, March 2015
- Behler, Jörg
- International Journal of Quantum Chemistry, Vol. 115, Issue 16
Next generation interatomic potentials for condensed systems
journal, July 2014
- Handley, Christopher Michael; Behler, Jörg
- The European Physical Journal B, Vol. 87, Issue 7
Graph kernels for chemical informatics
journal, October 2005
- Ralaivola, Liva; Swamidass, Sanjay J.; Saigo, Hiroto
- Neural Networks, Vol. 18, Issue 8
Moment Tensor Potentials: A Class of Systematically Improvable Interatomic Potentials
journal, January 2016
- Shapeev, Alexander V.
- Multiscale Modeling & Simulation, Vol. 14, Issue 3
Quantum-chemical insights from deep tensor neural networks
journal, January 2017
- Schütt, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan
- Nature Communications, Vol. 8, Issue 1
Ridge Regression: Biased Estimation for Nonorthogonal Problems
journal, February 1970
- Hoerl, Arthur E.; Kennard, Robert W.
- Technometrics, Vol. 12, Issue 1
Kernel methods in machine learning
journal, June 2008
- Hofmann, Thomas; Schölkopf, Bernhard; Smola, Alexander J.
- The Annals of Statistics, Vol. 36, Issue 3
An Efficiently Computable Graph-Based Metric for the Classification of Small Molecules
book, January 2008
- Schietgat, Leander; Ramon, Jan; Bruynooghe, Maurice
- Discovery Science
On Graph Kernels: Hardness Results and Efficient Alternatives
book, January 2003
- Gärtner, Thomas; Flach, Peter; Wrobel, Stefan
- Learning Theory and Kernel Machines
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
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
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
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
Applying machine learning techniques to predict the properties of energetic materials
journal, June 2018
- Elton, Daniel C.; Boukouvalas, Zois; Butrico, Mark S.
- Scientific Reports, Vol. 8, Issue 1
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
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
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
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
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
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
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
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
Efficient nonparametric -body force fields from machine learning
journal, May 2018
- Glielmo, Aldo; Zeni, Claudio; De Vita, Alessandro
- Physical Review B, Vol. 97, Issue 18
Machine Learning a General-Purpose Interatomic Potential for Silicon
journal, December 2018
- Bartók, Albert P.; Kermode, James; Bernstein, Noam
- Physical Review X, Vol. 8, Issue 4
Machine Learning a General-Purpose Interatomic Potential for Silicon
text, January 2018
- Bartók, Ap; Kermode, J.; Bernstein, N.
- Apollo - University of Cambridge Repository
Applying Machine Learning Techniques to Predict the Properties of Energetic Materials
posted_content, February 2018
- Elton, Daniel; Boukouvalas, Zois; Butrico, Mark S.
- ChemRxiv
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
Applying Machine Learning Techniques to Predict the Properties of Energetic Materials
posted_content, February 2018
- Elton, Daniel; Boukouvalas, Zois; Butrico, Mark S.
- ChemRxiv
An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields
text, January 2017
- Tang, Yu-Hang; Zhang, Dongkun; Karniadakis, George Em
- arXiv
WACSF - Weighted Atom-Centered Symmetry Functions as Descriptors in Machine Learning Potentials
text, January 2017
- Gastegger, Michael; Schwiedrzik, Ludwig; Bittermann, Marius
- arXiv
Efficient nonparametric $n$-body force fields from machine learning
text, January 2018
- Glielmo, Aldo; Zeni, Claudio; De Vita, Alessandro
- arXiv