Inferencia bayesiana asistida por modelos subrogados para el análisis de la cuantificación de la incertidumbre en problemas de ingeniería de cálculo intensivo

Zusammenfassung

This thesis is situated within the realm of Uncertainty Quantification, a multidisciplinary field with a pronounced practical orientation that integrates concepts from various disciplines such as Applied Mathematics, Engineering, Computer Science, and Statistics. Uncertainty Quantification can be defined as the process of analysing the uncertainties associated with predictions based on mathematical models. One of the primary challenges inherent in such analyses is that a significant part of the models employed in engineering are highly computationally demanding, rendering many common analysis techniques such as Monte Carlo simulation or MCMC algorithms unfeasible. A strategy capable of overcoming these difficulties involves substituting the forward models with metamodels, i.e., computationally lightweight approximations of the original model. However, in practical environments, ill-conditioned problems and nonlinear behaviours of the involved models are common, compromising the effectiveness of the proposed approach. Additionally, many phenomena incorporate intrinsic uncertainty that is not directly observable or measurable, whose nature requires the use of stochastic simulators, adding a layer of difficulty to the statistical treatment of the problem at hand. This research addresses the analysis of uncertainty within the framework of complex engineering problems that face the aforementioned challenges. To this end, various metamodels capable of efficiently replacing the computationally intensive original models will be proposed. Additionally, a new technique for constructing metamodels in stochastic contexts will be presented.