Consideration for the application of artificial neural networks to criticality code validation - 14270
The artificial neural network (ANN) is a consistent example for non-parametric parameter estimation and regression, with powerful universal approximation properties, that is distribution independent. ANN application to criticality code validation centers on aligning mathematical relationships between code validation parameters and neural network prediction for those parameter values. Two specific goals are: (1) an appropriate ANN architecture to determine validation parameter values, and (2) bootstrapping individual ANNs as a 'Prediction Interval' (PI) technique to estimate the Calculation Margin and Upper Subcritical Limit. The individual ANN workflow is segregated into Training, Validation (network), and Testing Sets, where the network predictive properties and performance are expressed in the latter set. The Bootstrap ANN replicates a large set of individual ANNs (taken from the original data distribution) where (1-α/2)100% PI estimates can be determined. Results from the ANN method are compared to a variety of validation examples: a 'toy example' from ANSI/ANS-8.24, Appendix D, a variety of methods noted in a Nuclear Criticality Safety Division 2009 paper, and several validation campaigns for highly enriched uranium and plutonium systems. The ANN method is robust and can be applied to single or multivariate inputs. A trained ANN can provide both an average estimate (e.g., single value) and an estimate over a range of independent variable values where the kUSL can be formed in a regression relationship suitable for extrapolation. The input dependence has been tested, ranging from 15 to over 400 sample size distributions. An expanded Shapiro-Wilk test (for sample sizes up to 5000) was implemented to confirm that the ANN method is transparent to distribution function. The Principle Component Analysis method was applied as an input preprocessing step embedded within the ANN in order to reduce dimensionality and correlation for multivariable inputs. This can potentially aid in determining accurate margins over applying arbitrary margins. The automatic optimization of the Bootstrap ANN PI is left for future consideration. (authors)