Uncertainty Quantification and Management for Multi-scale Nuclear Materials Modeling Nuclear Energy Advanced Modeling and Simulation

To validate multiscale simulation models, it is necessary to consider evidence collected at a length scale that is different from the one at which a model predicts. In addition, epistemic and aleatory uncertainties need to be distinguished for more robust decision making. In this study, a Bayesian approach with generalized interval probability is taken for model parameter validation. A generalized interval Bayes’ rule (GIBR) is used to combine the evidence and update belief in the validity of parameters. The sensitivity of completeness and soundness for interval range estimation in GIBR is investigated in comparison with Monte Carlo sampling. The method is first applied to validate the parameter set for a molecular dynamics simulation of defect formation due to radiation. It is then applied to combining the evidence from two models of crystal plasticity at different length scales. Summary of the Study Traditionally, sensitivity analysis is performed to assess the impact of epistemic uncertainty for modeling. Various methods such as variance-based global sensitivity analysis, local sensitivity analysis, Monte Carlo sampling, etc. have been developed. However, extensive computations are typically required in these methods to obtain the extent of variation. This prohibits their wide applications in large-scale simulations where each run of simulation is already costly. Alternatives such as Dempster-Shafer evidence theory, imprecise probability, random set, etc. have been developed to explicitly differentiate aleatory and epistemic uncertainty. As an extension of traditional probability theory, these approaches quantify uncertainty as a set of probability values. However, estimating the lower and upper bounds of