Improving accuracy and compensating for uncertainty in surrogate modeling

In most engineering fields, numerical simulators are used to model complex phenomena and obtain high-fidelity analysis. Despite the growth of computer capabilities, such simulators are limited by their computational cost. Surrogate modeling is a popular method to limit the computational expense. It consists of replacing the expensive model by a simpler model (surrogate) fitted to a few chosen simulations at a set of points called a design of experiments (DoE).;By definition, a surrogate model contains uncertainties, since it is an approximation to an unknown function. A surrogate inherits uncertainties from two main sources: uncertainty in the observations (when they are noisy), and uncertainty due to finite sample. One of the major challenges in surrogate modeling consists of controlling and compensating for these uncertainties. Two classical frameworks of surrogate application are used as a discussion thread for this research: constrained optimization and reliability analysis.;In this work, we propose alternatives to compensate for the surrogate model errors in order to obtain safe predictions with minimal impact on the accuracy. The methods are based on different error estimation techniques, some based on statistical assumptions and some that are non-parametric. Their efficiency are analyzed for general prediction and for the approximation of reliability measures.;We also propose two contributions to the field of design of experiments in order to minimize the uncertainty of surrogate models. Firstly, we address the issue of choosing the experiments when surrogates are used for reliability assessment and constrained optimization. Secondly, we propose global sampling strategies to answer the issue of allocating limited computational resource in the context of RBDO.;All methods are supported by quantitative results on simple numerical examples and engineering applications. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)...