Bias Minimization in Gaussian Process Surrogatemodeling for Uncertainty Quantification

Uncertainty quantification analyses often employ surrogate models as computationally efficient approximations of computer codes simulating the physical phenomena. The accuracy and economy in the construction of surrogate models depends on the quality and quantity of data collected from the computationally expensive system models. Computationally efficient methods for accurate surrogate model training are thus required. This paper develops a novel approach to surrogate model construction based on the hierarchical decomposition of the approximation error. The proposed algorithm employs sparse Gaussian processes on a hierarchical grid to achieve a sparse nonlinear approximation of the underlying function. In contrast to existing methods, which are based on minimizing prediction variance, the proposed approach focuses on model bias and aims to improve the quality of reconstruction represented by the model. The performance of the algorithm is compared to existing methods using several numerical examples. In the examples considered, the proposed method demonstrates significant improvement in the quality of reconstruction for the same sample size.