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Title: The F-t-Pj-RG method: An adjacent-rolling-windows based steady-state detection technique for application to kinetic Monte Carlo simulations

Abstract

A window-based steady-state detection algorithm has been developed for application to kinetic Monte Carlo simulation data. The algorithm, termed F-t-Pj-RG sequentially applies an F-test, a t-test, and a projection test on adjacent windows of the data while rolling (or shifting) and growing the windows when any of the tests fail. In aggregate, the algorithm is able to (a) automatically reject the warm-up period as not being at steady-state, as well as (b) determine an appropriate window size for converged statistics when sampling the data, which is necessary for detection of steady-state, and (c) detect steady-state within a particular tolerance. The last step, the projection test, is actually an oscillating-slope projection test, and is performed on j sequential data windows (i.e., more than two adjacent windows). It requires more than simply being within the user defined tolerance: the oscillating-slope projection test includes a condition that the slope must oscillate around zero when 2, which is an additional indication of steady-state. When all three tests are passed, the F-t-Pj test is passed, indicating that the prerequisites of steady-state detection have been met and also that conditions consistent with the definition of steady-state have been realized. This algorithm is applied to a varietymore » of data sets that correspond to the diverse type of data trends that can be produced by kinetic Monte Carlo simulations. The algorithm is shown to be robust in its ability to handle differing functional forms, and is able to detect steady-state with low computational cost. Finally, the low computational cost of this method and its robustness towards varied data trends make it suitable for on-the-fly use in kinetic Monte Carlo simulations.« less

Authors:
 [1];  [2]; ORCiD logo [3];  [4]
  1. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Mechanical Engineering
  2. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Materials Science and Engineering
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Chemical Sciences Division
  4. Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Mechanical Engineering; Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Materials Science and Engineering
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1495967
Alternate Identifier(s):
OSTI ID: 1548150
Grant/Contract Number:  
AC05-00OR22725; LOIS 8457
Resource Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 232; Journal Issue: C; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Steady-state detection; Kinetic Monte Carlo simulations; Complex chemical reactions

Citation Formats

Nellis, Chris, Danielson, Thomas, Savara, Aditya, and Hin, Celine. The F-t-Pj-RG method: An adjacent-rolling-windows based steady-state detection technique for application to kinetic Monte Carlo simulations. United States: N. p., 2018. Web. doi:10.1016/j.cpc.2018.05.013.
Nellis, Chris, Danielson, Thomas, Savara, Aditya, & Hin, Celine. The F-t-Pj-RG method: An adjacent-rolling-windows based steady-state detection technique for application to kinetic Monte Carlo simulations. United States. https://doi.org/10.1016/j.cpc.2018.05.013
Nellis, Chris, Danielson, Thomas, Savara, Aditya, and Hin, Celine. Sat . "The F-t-Pj-RG method: An adjacent-rolling-windows based steady-state detection technique for application to kinetic Monte Carlo simulations". United States. https://doi.org/10.1016/j.cpc.2018.05.013. https://www.osti.gov/servlets/purl/1495967.
@article{osti_1495967,
title = {The F-t-Pj-RG method: An adjacent-rolling-windows based steady-state detection technique for application to kinetic Monte Carlo simulations},
author = {Nellis, Chris and Danielson, Thomas and Savara, Aditya and Hin, Celine},
abstractNote = {A window-based steady-state detection algorithm has been developed for application to kinetic Monte Carlo simulation data. The algorithm, termed F-t-Pj-RG sequentially applies an F-test, a t-test, and a projection test on adjacent windows of the data while rolling (or shifting) and growing the windows when any of the tests fail. In aggregate, the algorithm is able to (a) automatically reject the warm-up period as not being at steady-state, as well as (b) determine an appropriate window size for converged statistics when sampling the data, which is necessary for detection of steady-state, and (c) detect steady-state within a particular tolerance. The last step, the projection test, is actually an oscillating-slope projection test, and is performed on j sequential data windows (i.e., more than two adjacent windows). It requires more than simply being within the user defined tolerance: the oscillating-slope projection test includes a condition that the slope must oscillate around zero when 2, which is an additional indication of steady-state. When all three tests are passed, the F-t-Pj test is passed, indicating that the prerequisites of steady-state detection have been met and also that conditions consistent with the definition of steady-state have been realized. This algorithm is applied to a variety of data sets that correspond to the diverse type of data trends that can be produced by kinetic Monte Carlo simulations. The algorithm is shown to be robust in its ability to handle differing functional forms, and is able to detect steady-state with low computational cost. Finally, the low computational cost of this method and its robustness towards varied data trends make it suitable for on-the-fly use in kinetic Monte Carlo simulations.},
doi = {10.1016/j.cpc.2018.05.013},
journal = {Computer Physics Communications},
number = C,
volume = 232,
place = {United States},
year = {2018},
month = {6}
}

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Figures / Tables:

Figure 1 Figure 1: Anticipated trends in the EFs from KMC simulations a) rising exponential, b) falling exponential, c) "immediate steady-state", d) rare-events (or "spikey" data), e) undulating steadystate and f) infinitely-rising. Each of these trends will need to be properly treated by the steadystate dection algorithm.

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Works referencing / citing this record:

A Practical Guide to Surface Kinetic Monte Carlo Simulations
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