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PhD defense of Neissrien Alhubieshi

Title: Global Sensitivity Analysis with Surrogate Modeling

PhD advisor: Yaning Liu

Date and time: July 21, 2022 from 10am-12pm

Location: Student Commons Building-ACAD-4119 classroom

PhD committee: Jan Mandel (Committee Chair), Yaning Liu (PhD Advisor), Julien Langou, Burt Simon, and Liang He.

Abstract: Global sensitivity analysis studies how uncertainties in the input factors of a model affect the output. In this dissertation, we first introduce the widely used variance-based Sobol’ global sensitivity analysis, where ANOVA decomposition-based indices measuring the sole contribution of a parameter and its interaction with the other parameters are used. These indices are typically estimated directly by Monte Carlo simulations, which can be computationally intractable especially for computationally expensive models. We then introduce the classical Fourier Amplitude Sensitivity Test (FAST) for computing Sobol’ global sensitivity indices. We propose using FAST as a surrogate model based on high dimensional model representation (HDMR) so that FAST can be used to not only estimate variance-based global sensitivity indices but also perform any tasks involved in uncertainty quantification. The accuracy of the resulting surrogate model, named FAST-HDMR, can be improved by various techniques. We show that sparse regression techniques, such as relevance vector machine and variational inference, which retain only the significant terms in the FAST-HDMR expansion, as well as advanced Monte Carlo sampling methods, such as randomized quasi-Monte Carlo sampling and variance-reduction techniques, can be utilized for that purpose. In addition, we present multi-fidelity methods for surrogate modeling to estimate global sensitivity indices that leverage low-fidelity models to reduce computational cost while maintaining the accuracy of the high-fidelity model. We propose computing global sensitivity indices based on the Proper Orthogonal Decomposition Mapping Method (PODMM), and show that it outperforms a recent multi- fidelity Monte Carlo algorithm through a few examples. We also illustrate how HDMR can be employed in the setting of multi-fidelity surrogate modeling for efficient global sensitivity analysis. Finally, we apply the proposed FAST-HDMR, PODMM and multi-fidelity HDMR approaches for global sensitivity analysis to two practical applications, where parameters’ global sensitivity information is needed.

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