TOWARDS OVERCOMING THE CURSE OF DIMENSIONALITY IN PREDICTIVE MODELLING AND UNCERTAINTY QUANTIFICATION

Abstract

This invited presentation summarizes new methodologies developed by the author for performing high-order sensitivity analysis, uncertainty quantification and predictive modeling. The presentation commences by summarizing the newly developed 3rd-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for linear systems, which overcomes the “curse of dimensionality” for sensitivity analysis and uncertainty quantification of a large variety of model responses of interest in reactor physics systems. The use of the exact expressions of the 2nd-, and 3rd-order sensitivities computed using the 3rd-ASAM is subsequently illustrated by presenting 3rd-order formulas for the first three cumulants of the response distribution, for quantifying response uncertainties (covariance, skewness) stemming from model parameter uncertainties. The use of the 1st-, 2nd-, and 3rd-order sensitivities together with the formulas for the first three cumulants of the response distribution are subsequently used in the newly developed 2nd/3rd-BERRU-PM (“Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”), which aims at overcoming the curse of dimensionality in predictive modeling. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing a subjective user-defined “cost functional quantifying the discrepancies between measurements and computations.” By utilizing the 1st-, 2nd- and 3rd-order response sensitivities to combine experimental and computational information in the joint phase-space of responses and model parameters, the 2nd/3rd-BERRU-PM generalizes the current data adjustment/assimilation methodologies. Even though all of the 2nd- and 3rd-order are comprised in the mathematical framework of the 2nd/3rd-BERRU-PM formalism, the computations underlying the 2nd/3rd-BERRU-PM require the inversion of a single matrix of dimensions equal to the number of considered responses, thus overcoming the curse of dimensionality which would affect the inversion of hessian and higher-order matrices in the parameter space.