# Nudged elastic band calculations accelerated with Gaussian process regression

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**Nudged elastic band calculations accelerated with Gaussian process regression.** / Koistinen, Olli-Pekka; Dagbjartsdóttir, Freyja B.; Ásgeirsson, Vilhjálmur; Vehtari, Aki; Jonsson, Hannes.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Journal of Chemical Physics*, vol. 147, no. 15, 152720, pp. 1-14. https://doi.org/10.1063/1.4986787

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*Journal of Chemical Physics*,

*147*(15), 1-14. [152720]. https://doi.org/10.1063/1.4986787

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TY - JOUR

T1 - Nudged elastic band calculations accelerated with Gaussian process regression

AU - Koistinen, Olli-Pekka

AU - Dagbjartsdóttir, Freyja B.

AU - Ásgeirsson, Vilhjálmur

AU - Vehtari, Aki

AU - Jonsson, Hannes

PY - 2017/10/21

Y1 - 2017/10/21

N2 - Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The computational effort can be large, especially when ab initio or electron density functional calculations are used to evaluate the energy and atomic forces. Here, we show how the number of such evaluations can be reduced by an order of magnitude using a Gaussian process regression approach where an approximate energy surface is generated and refined in each iteration. When the goal is to evaluate the transition rate within harmonic transition state theory, the evaluation of the Hessian matrix at the initial and final state minima can be carried out beforehand and used as input in the minimum energy path calculation, thereby improving stability and reducing the number of iterations needed for convergence. A Gaussian process model also provides an uncertainty estimate for the approximate energy surface, and this can be used to focus the calculations on the lesser-known part of the path, thereby reducing the number of needed energy and force evaluations to a half in the present calculations. The methodology is illustrated using the two-dimensional Müller-Brown potential surface and performance assessed on an established benchmark involving 13 rearrangement transitions of a heptamer island on a solid surface.

AB - Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The computational effort can be large, especially when ab initio or electron density functional calculations are used to evaluate the energy and atomic forces. Here, we show how the number of such evaluations can be reduced by an order of magnitude using a Gaussian process regression approach where an approximate energy surface is generated and refined in each iteration. When the goal is to evaluate the transition rate within harmonic transition state theory, the evaluation of the Hessian matrix at the initial and final state minima can be carried out beforehand and used as input in the minimum energy path calculation, thereby improving stability and reducing the number of iterations needed for convergence. A Gaussian process model also provides an uncertainty estimate for the approximate energy surface, and this can be used to focus the calculations on the lesser-known part of the path, thereby reducing the number of needed energy and force evaluations to a half in the present calculations. The methodology is illustrated using the two-dimensional Müller-Brown potential surface and performance assessed on an established benchmark involving 13 rearrangement transitions of a heptamer island on a solid surface.

UR - https://arxiv.org/abs/1706.04606

U2 - 10.1063/1.4986787

DO - 10.1063/1.4986787

M3 - Article

VL - 147

SP - 1

EP - 14

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 15

M1 - 152720

ER -

ID: 14167287