Forward uncertainty quantification is used to obtain useful insight of many physical models. However, it is a challenge to get accurate results for a given amount of computational resources, when dealing with complex models. There are different methods to tackle such problems. In this work we combine two of such techniques namely, polynomial chaos expansion and multi-fidelity to create an efficient method to solve forward UQ problems. Firstly, we develop multi-fidelity Gaussian process regression models which fuse information from the low-fidelity model, derivative approximations of it and the parameter space. We also use a composite kernel which further improves the regression results. Thereafter, those models request adaptively new high-fidelity data points which improve the currently existing surrogate the best. Finally, we perform polynomial chaos expansion on Gaussian process surrogates to estimate the statistical moments of a quantity of interest. Combining the aforementioned methods leads to an efficient approach for solving forward UQ problems. In this work, we deal with only two level of fidelity. Our evaluation of the method shows considerable savings of computational effort.

Keywords: Multifidelity, Gaussian processes, Polynomial chaos expansion, forward UQ problems