# Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

## Abstract

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric. This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1234327

- Report Number(s):
- ORNL/SPR-2015/107

DP4015051; NADP206

- DOE Contract Number:
- AC05-00OR22725

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Bledsoe, Keith C.
```*Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling*. United States: N. p., 2015.
Web. doi:10.2172/1234327.

```
Bledsoe, Keith C.
```*Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling*. United States. doi:10.2172/1234327.

```
Bledsoe, Keith C. Wed .
"Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling". United States.
doi:10.2172/1234327. https://www.osti.gov/servlets/purl/1234327.
```

```
@article{osti_1234327,
```

title = {Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling},

author = {Bledsoe, Keith C.},

abstractNote = {The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric. This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.},

doi = {10.2172/1234327},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Apr 01 00:00:00 EDT 2015},

month = {Wed Apr 01 00:00:00 EDT 2015}

}