# GPU Acceleration of Mean Free Path Based Kernel Density Estimators for Monte Carlo Neutronics Simulations

## Abstract

Kernel Density Estimators (KDEs) are a non-parametric density estimation technique that has recently been applied to Monte Carlo radiation transport simulations. Kernel density estimators are an alternative to histogram tallies for obtaining global solutions in Monte Carlo tallies. With KDEs, a single event, either a collision or particle track, can contribute to the score at multiple tally points with the uncertainty at those points being independent of the desired resolution of the solution. Thus, KDEs show potential for obtaining estimates of a global solution with reduced variance when compared to a histogram. Previously, KDEs have been applied to neutronics for one-group reactor physics problems and fixed source shielding applications. However, little work was done to obtain reaction rates using KDEs. This paper introduces a new form of the MFP KDE that is capable of handling general geometries. Furthermore, extending the MFP KDE to 2-D problems in continuous energy introduces inaccuracies to the solution. An ad-hoc solution to these inaccuracies is introduced that produces errors smaller than 4% at material interfaces.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- Contributing Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)

- OSTI Identifier:
- 1226887

- Report Number(s):
- LA-UR-15-29020

TRN: US1500899

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; 97 MATHEMATICS AND COMPUTING; MONTE CARLO METHOD; MATHEMATICAL SOLUTIONS; KERNELS; MEAN FREE PATH; COMPUTERIZED SIMULATION; COMPARATIVE EVALUATIONS; REACTION KINETICS; CALCULATION METHODS; NEUTRON TRANSPORT; ACCURACY; DATA COVARIANCES; INTERFACES; RESOLUTION; TWO-DIMENSIONAL CALCULATIONS; SLABS; ONE-DIMENSIONAL CALCULATIONS; ALGORITHMS; OPTIMIZATION; KDE; OpenMC

### Citation Formats

```
Burke, TImothy P., Kiedrowski, Brian C., Martin, William R., and Brown, Forrest B.
```*GPU Acceleration of Mean Free Path Based Kernel Density Estimators for Monte Carlo Neutronics Simulations*. United States: N. p., 2015.
Web. doi:10.2172/1226887.

```
Burke, TImothy P., Kiedrowski, Brian C., Martin, William R., & Brown, Forrest B.
```*GPU Acceleration of Mean Free Path Based Kernel Density Estimators for Monte Carlo Neutronics Simulations*. United States. doi:10.2172/1226887.

```
Burke, TImothy P., Kiedrowski, Brian C., Martin, William R., and Brown, Forrest B. Thu .
"GPU Acceleration of Mean Free Path Based Kernel Density Estimators for Monte Carlo Neutronics Simulations". United States. doi:10.2172/1226887. https://www.osti.gov/servlets/purl/1226887.
```

```
@article{osti_1226887,
```

title = {GPU Acceleration of Mean Free Path Based Kernel Density Estimators for Monte Carlo Neutronics Simulations},

author = {Burke, TImothy P. and Kiedrowski, Brian C. and Martin, William R. and Brown, Forrest B.},

abstractNote = {Kernel Density Estimators (KDEs) are a non-parametric density estimation technique that has recently been applied to Monte Carlo radiation transport simulations. Kernel density estimators are an alternative to histogram tallies for obtaining global solutions in Monte Carlo tallies. With KDEs, a single event, either a collision or particle track, can contribute to the score at multiple tally points with the uncertainty at those points being independent of the desired resolution of the solution. Thus, KDEs show potential for obtaining estimates of a global solution with reduced variance when compared to a histogram. Previously, KDEs have been applied to neutronics for one-group reactor physics problems and fixed source shielding applications. However, little work was done to obtain reaction rates using KDEs. This paper introduces a new form of the MFP KDE that is capable of handling general geometries. Furthermore, extending the MFP KDE to 2-D problems in continuous energy introduces inaccuracies to the solution. An ad-hoc solution to these inaccuracies is introduced that produces errors smaller than 4% at material interfaces.},

doi = {10.2172/1226887},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {11}

}