Stability and convergence of the string method for computing minimum energy paths∗

Brian Van Koten; Mitchell Luskin

doi:10.1137/18M1201032

Stability and convergence of the string method for computing minimum energy paths^∗

Brian Van Koten, Mitchell Luskin

Mathematics

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

1 Scopus citations

Abstract

We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.

Original language	English (US)
Pages (from-to)	873-898
Number of pages	26
Journal	Multiscale Modeling and Simulation
Volume	17
Issue number	2
DOIs	https://doi.org/10.1137/18M1201032
State	Published - 2019

Bibliographical note

Funding Information:
∗Received by the editors July 17, 2018; accepted for publication (in revised form) May 14, 2019; published electronically June 27, 2019. http://www.siam.org/journals/mms/17-2/M120103.html Funding: The first author was supported by the NSF RTG: Computational and Applied Mathematics in Statistical Science, award number 1547396. The second author was partly supported by the U.S. Department of Energy Office of Science, grant DE-SC0012733, and the Simons Foundation. †University of Massachusetts, Amherst, MA, 01003-9305 (bvankoten@gmail.com). ‡School of Mathematics, University of Minnesota, Minneapolis, MN, 55455 (luskin@umn.edu).

Keywords

Convergence
Minimum energy path
Stability
String method

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title = "Stability and convergence of the string method for computing minimum energy paths∗ ",

abstract = "We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.",

keywords = "Convergence, Minimum energy path, Stability, String method",

author = "Koten, {Brian Van} and Mitchell Luskin",

note = "Funding Information: ∗Received by the editors July 17, 2018; accepted for publication (in revised form) May 14, 2019; published electronically June 27, 2019. http://www.siam.org/journals/mms/17-2/M120103.html Funding: The first author was supported by the NSF RTG: Computational and Applied Mathematics in Statistical Science, award number 1547396. The second author was partly supported by the U.S. Department of Energy Office of Science, grant DE-SC0012733, and the Simons Foundation. †University of Massachusetts, Amherst, MA, 01003-9305 (bvankoten@gmail.com). ‡School of Mathematics, University of Minnesota, Minneapolis, MN, 55455 (luskin@umn.edu).",

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T1 - Stability and convergence of the string method for computing minimum energy paths∗

AU - Koten, Brian Van

AU - Luskin, Mitchell

N1 - Funding Information: ∗Received by the editors July 17, 2018; accepted for publication (in revised form) May 14, 2019; published electronically June 27, 2019. http://www.siam.org/journals/mms/17-2/M120103.html Funding: The first author was supported by the NSF RTG: Computational and Applied Mathematics in Statistical Science, award number 1547396. The second author was partly supported by the U.S. Department of Energy Office of Science, grant DE-SC0012733, and the Simons Foundation. †University of Massachusetts, Amherst, MA, 01003-9305 (bvankoten@gmail.com). ‡School of Mathematics, University of Minnesota, Minneapolis, MN, 55455 (luskin@umn.edu).

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N2 - We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.

AB - We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden [J. Chem. Phys., 126 (2007), 164103] to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.

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