Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model

Garrido Torres, José A.; Jennings, Paul C.; Hansen, Martin H.; Boes, Jacob R.; Bligaard, Thomas

doi:10.1103/physrevlett.122.156001

Title: Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model

Abstract

We present the incorporation of a surrogate Gaussian process regression (GPR) atomistic model to greatly accelerate the rate of convergence of classical nudged elastic band (NEB) calculations. In our surrogate model approach, the cost of converging the elastic band no longer scales with the number of moving images on the path. This provides a far more efficient and robust transition state search. In contrast to a conventional NEB calculation, the algorithm presented here eliminates any need for manipulating the number of images to obtain a converged result. This is achieved by inventing a new convergence criteria that exploits the probabilistic nature of the GPR to use uncertainty estimates of all images in combination with the force in the saddle point in the target model potential. In conclusion, our method is an order of magnitude faster in terms of function evaluations than the conventional NEB method with no accuracy loss for the converged energy barrier values.

Authors:

Garrido Torres, José A. ^[1]; Jennings, Paul C. ^[1]; Hansen, Martin H. ^[1]; Boes, Jacob R. ^[1]; Bligaard, Thomas ^[2]

Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:: Mon Apr 15 00:00:00 EDT 2019

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1526444

Alternate Identifier(s):: OSTI ID: 1507189

Grant/Contract Number:: AC02-76SF00515

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 122; Journal Issue: 15; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Garrido Torres, José A., Jennings, Paul C., Hansen, Martin H., Boes, Jacob R., and Bligaard, Thomas. Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model.  United States: N. p., 2019. 
Web.  doi:10.1103/physrevlett.122.156001.

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                    Garrido Torres, José A., Jennings, Paul C., Hansen, Martin H., Boes, Jacob R., & Bligaard, Thomas. Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model.  United States.  https://doi.org/10.1103/physrevlett.122.156001

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                    Garrido Torres, José A., Jennings, Paul C., Hansen, Martin H., Boes, Jacob R., and Bligaard, Thomas. Mon .  
"Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model".  United States.  https://doi.org/10.1103/physrevlett.122.156001.  https://www.osti.gov/servlets/purl/1526444.

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@article{osti_1526444,

  title        = {Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model},

  author       = {Garrido Torres, José A. and Jennings, Paul C. and Hansen, Martin H. and Boes, Jacob R. and Bligaard, Thomas},

  abstractNote = {We present the incorporation of a surrogate Gaussian process regression (GPR) atomistic model to greatly accelerate the rate of convergence of classical nudged elastic band (NEB) calculations. In our surrogate model approach, the cost of converging the elastic band no longer scales with the number of moving images on the path. This provides a far more efficient and robust transition state search. In contrast to a conventional NEB calculation, the algorithm presented here eliminates any need for manipulating the number of images to obtain a converged result. This is achieved by inventing a new convergence criteria that exploits the probabilistic nature of the GPR to use uncertainty estimates of all images in combination with the force in the saddle point in the target model potential. In conclusion, our method is an order of magnitude faster in terms of function evaluations than the conventional NEB method with no accuracy loss for the converged energy barrier values.},

  doi          = {10.1103/physrevlett.122.156001},

  journal      = {Physical Review Letters},

  number       = 15,

  volume       = 122,

  place        = {United States},

  year         = {Mon Apr 15 00:00:00 EDT 2019},

  month        = {Mon Apr 15 00:00:00 EDT 2019}

}

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Title: Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model

Abstract

Citation Formats

Effect of the damping function in dispersion corrected density functional theory journal, March 2011

A doubly nudged elastic band method for finding transition states journal, February 2004

Generalized Gradient Approximation Made Simple journal, October 1996

On the limited memory BFGS method for large scale optimization journal, August 1989

Projector augmented-wave method journal, December 1994

Nudged elastic band method for finding minimum energy paths of transitions conference, November 2011

Atomic Energies from a Convolutional Neural Network journal, May 2018

Amp: A modular approach to machine learning in atomistic simulations journal, October 2016

Exploration versus Exploitation in Global Atomistic Structure Optimization journal, January 2018

Structural Relaxation Made Simple journal, October 2006

Nudged elastic band calculations accelerated with Gaussian process regression journal, October 2017

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials journal, September 2009

An automated nudged elastic band method journal, September 2016

The atomic simulation environment—a Python library for working with atoms journal, June 2017

The SIESTA method for ab initio order- N materials simulation journal, March 2002

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

Searching for Saddle Points by Using the Nudged Elastic Band Method: An Implementation for Gas-Phase Systems journal, May 2006

From ultrasoft pseudopotentials to the projector augmented-wave method journal, January 1999

First-principles simulation: ideas, illustrations and the CASTEP code journal, March 2002

Interatomic interactions in the effective-medium theory journal, May 1987

Inhomogeneous Electron Gas journal, November 1964

Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method journal, June 2010

Paths to which the nudged elastic band converges journal, February 2011

Adaptive nudged elastic band approach for transition state calculation journal, September 2002

Acceleration of saddle-point searches with machine learning journal, August 2016

A climbing image nudged elastic band method for finding saddle points and minimum energy paths journal, December 2000

A super-linear minimization scheme for the nudged elastic band method journal, December 2003

Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points journal, December 2000

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu journal, April 2010

A generalized solid-state nudged elastic band method journal, February 2012

A growing string method for determining transition states: Comparison to the nudged elastic band and string methods journal, May 2004

Self-Consistent Equations Including Exchange and Correlation Effects journal, November 1965

Tuning the activities of cuprous oxide nanostructures via the oxide-metal interaction journal, May 2020

Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets journal, May 2021

Electronic structure of AlFeN films exhibiting crystallographic orientation change from c- to a-axis with Fe concentrations and annealing effect journal, February 2020

Nudged elastic band calculations accelerated with Gaussian process regression text, January 2017

A Doubly Nudged Elastic Band Method for Finding Transition States text, January 2004

Catalysis-Hub.org, an open electronic structure database for surface reactions journal, May 2019

Predicting metal–metal interactions. I. The influence of strain on nanoparticle and metal adlayer stabilities journal, March 2020

Constructing convex energy landscapes for atomistic structure optimization journal, December 2019

A local Bayesian optimizer for atomic structures text, January 2018

Effect of the damping function in dispersion corrected density functional theory
journal, March 2011

A doubly nudged elastic band method for finding transition states
journal, February 2004

Generalized Gradient Approximation Made Simple
journal, October 1996

On the limited memory BFGS method for large scale optimization
journal, August 1989

Projector augmented-wave method
journal, December 1994

Nudged elastic band method for finding minimum energy paths of transitions
conference, November 2011

Atomic Energies from a Convolutional Neural Network
journal, May 2018

Amp: A modular approach to machine learning in atomistic simulations
journal, October 2016

Exploration versus Exploitation in Global Atomistic Structure Optimization
journal, January 2018

Structural Relaxation Made Simple
journal, October 2006

Nudged elastic band calculations accelerated with Gaussian process regression
journal, October 2017

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

An automated nudged elastic band method
journal, September 2016

The atomic simulation environment—a Python library for working with atoms
journal, June 2017

The SIESTA method for ab initio order- N materials simulation
journal, March 2002

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

Searching for Saddle Points by Using the Nudged Elastic Band Method: An Implementation for Gas-Phase Systems
journal, May 2006

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

First-principles simulation: ideas, illustrations and the CASTEP code
journal, March 2002

Interatomic interactions in the effective-medium theory
journal, May 1987

Inhomogeneous Electron Gas
journal, November 1964

Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method
journal, June 2010

Paths to which the nudged elastic band converges
journal, February 2011

Adaptive nudged elastic band approach for transition state calculation
journal, September 2002

Acceleration of saddle-point searches with machine learning
journal, August 2016

A climbing image nudged elastic band method for finding saddle points and minimum energy paths
journal, December 2000

A super-linear minimization scheme for the nudged elastic band method
journal, December 2003

Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
journal, December 2000

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
journal, April 2010

A generalized solid-state nudged elastic band method
journal, February 2012

A growing string method for determining transition states: Comparison to the nudged elastic band and string methods
journal, May 2004

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

Tuning the activities of cuprous oxide nanostructures via the oxide-metal interaction
journal, May 2020

Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets
journal, May 2021

Electronic structure of AlFeN films exhibiting crystallographic orientation change from c- to a-axis with Fe concentrations and annealing effect
journal, February 2020

Nudged elastic band calculations accelerated with Gaussian process regression
text, January 2017

A Doubly Nudged Elastic Band Method for Finding Transition States
text, January 2004

Catalysis-Hub.org, an open electronic structure database for surface reactions
journal, May 2019

Predicting metal–metal interactions. I. The influence of strain on nanoparticle and metal adlayer stabilities
journal, March 2020

Constructing convex energy landscapes for atomistic structure optimization
journal, December 2019

A local Bayesian optimizer for atomic structures
text, January 2018