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

University of South Carolina 300 Main Street, Columbia, SC 29208, USA

cacuci@cec.sc.edu

Published online: 22 February 2021

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 3^rd-Order Adjoint Sensitivity Analysis Methodology (3^rd-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 2^nd-, and 3^rd-order sensitivities computed using the 3^rd-ASAM is subsequently illustrated by presenting 3^rd-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-, 2^nd-, and 3^rd-order sensitivities together with the formulas for the first three cumulants of the response distribution are subsequently used in the newly developed 2^nd/3^rd-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 2^nd/3^rd-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-, 2^nd- and 3^rd-order response sensitivities to combine experimental and computational information in the joint phase-space of responses and model parameters, the 2^nd/3^rd-BERRU-PM generalizes the current data adjustment/assimilation methodologies. Even though all of the 2^nd- and 3^rd-order are comprised in the mathematical framework of the 2^nd/3^rd-BERRU-PM formalism, the computations underlying the 2^nd/3^rd-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.