A Bayesian Approach for Global Sensitivity Analysis of (Multifidelity) Computer Codes

Abstract

Complex computer codes are widely used in science and engineering to model physical phenomena. Furthermore, it is common that they have a large number of input parameters. Global sensitivity analysis aims to identify those which have the most important impact on the output. Sobol indices are a popular tool to perform such analysis. However, their estimations require an important number of simulations and often cannot be processed under reasonable time constraint. To handle this problem, a Gaussian process regression model is built to surrogate the computer code and the Sobol indices are estimated through it. The aim of this paper is to provide a methodology to estimate the Sobol indices through a surrogate model taking into account both the estimation errors and the surrogate model errors. In particular, it allows us to derive non-asymptotic confidence intervals for the Sobol index estimations. Furthermore, we extend the suggested strategy to the case of multi-fidelity computer codes which can be run at different levels of accuracy. For such simulators, we use an extension of Gaussian process regression models for multivariate outputs.

Metamodel-Based Sensitivity Analysis: Polynomial Chaos Expansions and Gaussian Processes

“…To do so, one can use the central limit theorem [31; 17] or a bootstrap procedure [34]. In particular, a methodology to evaluate the uncertainty on the sensitivity index due to both the Gaussian process and to the pick-freeze approximations is presented in Le Gratiet et al [34].…”

“…Recent developments in which metamodeling errors are taken into account in the analysis have been proposed by Le Gratiet et al [34]; Chastaing and Le Gratiet [17].…”

Bayesian Sensitivity Analysis of Flight Parameters in a Hard-Landing Analysis Process

“…For example, the method presented in [22] considers multidelity computer codes and is implemented in the R package "sensitivity". In addition, the tgp package [23] oers a greater exibility by generalising GPs using regression trees, allowing emulation of nonstationary models and bifurcating responses [24].…”

Sensitivity analysis via Karhunen–Loève expansion of a random field model: Estimation of Sobol’ indices and experimental design

“…In case of functions f(·) of computationally expensive evaluation, the use of metamodels, possibly combined with Monte-Carlo sampling, allows estimation of indices from a reduced number of data points; see e.g., [25,23,20]. The calculation of Sobol' indices is then considerably facilitated when the metamodel used has a particular form, which is especially adapted to the underlying Sobol'-Hoeding decomposition.…”