Accurate construction of high dimensional model representation with applications to uncertainty quantification

Surrogate modeling is a popular and practical method to meet the needs of a large number of queries of computationally demanding models in the analysis of uncertainty, sensitivity and system reliability. We explore various methods that can improve the accuracy of a particular class of surrogate models, the high dimensional model representation (HDMR), and their performances in uncertainty quantification and variance-based global sensitivity analysis. Rigorous analysis is provided to show the equivalence of the two common types of HDMRs-Cut-HDMR and random sampling-HDMR (RS-HDMR), when they are the same order of truncation. We propose using the nodes of Gauss and Clenshaw-Curtis quadratures as the interpolation points for the construction of Cut-HDMR to achieve high (spectral) accuracy for both the surrogate model and global sensitivity indices. As for RS-HDMR, randomized quasi-Monte Carlo sampling with variance reduction techniques, coupled with a procedure to select the optimal polynomial orders and prune potential noise terms, is shown to be capable of effectively enhancing the model accuracy. The efficiency of our proposed methods is demonstrated by a few analytical examples that are commonly studied for uncertainty and sensitivity analysis algorithms. Finally, we apply HDMR surrogate modeling techniques for an operational wildland fire model that is widely employed in fire prevention and safety control, and a chemical kinetics H2/air combustion model predicting the ignition delay time, which plays an important role in studying fuel and combustion system reliability and safety.