Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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Performing linear regression with responses calculated using Monte Carlo transport codes

  • Price, Dean (Department of Nuclear Engineering and Radiological Science, University of Michigan) ;
  • Kochunas, Brendan (Department of Nuclear Engineering and Radiological Science, University of Michigan)
  • Received : 2021.08.18
  • Accepted : 2021.11.03
  • Published : 2022.05.25
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Abstract

In many of the complex systems modeled in the field of nuclear engineering, it is often useful to use linear regression-based analyses to analyze relationships between model parameters and responses of interests. In cases where the response of interest is calculated by a simulation which uses Monte Carlo methods, there will be some uncertainty in the responses. Further, the reduction of this uncertainty increases the time necessary to run each calculation. This paper presents some discussion on how the Monte Carlo error in the response of interest influences the error in computed linear regression coefficients. A mathematical justification is given that shows that when performing linear regression in these scenarios, the error in regression coefficients can be largely independent of the Monte Carlo error in each individual calculation. This condition is only true if the total number of calculations are scaled to have a constant total time, or amount of work, for all calculations. An application with a simple pin cell model is used to demonstrate these observations in a practical problem.

Keywords

Acknowledgement

We would like to thank Professor Brian Kiedrowski and David Griesheimer for their helpful thoughts during our discussions concerning the subject of this work. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1256260.

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