BIAS MINIMIZATION IN GAUSSIAN PROCESS SURROGATE MODELING FOR UNCERTAINTY QUANTIFICATION

Abstract

Uncertainty quantification analyses often employ surrogate modelsas computationally efficient approximations of com- puter codes simulatingthe physical phenomena. The accuracy and economy in the constructionof surrogate models depends on the quality and quantity of data collectedfrom the computationally expensive system models. Computa- tionallyefficient methods for accurate surrogate model training are thusrequired. This paper develops a novel approach to surrogate modelconstruction based on the hierarchical decomposition of the approximationerror. The proposed al- gorithm employs sparse Gaussian processeson a hierarchical grid to achieve a sparse nonlinear approximationof the underlying function. In contrast to existing methods, whichare based on minimizing prediction variance, the proposed approachfocuses on model bias and aims to improve the quality of reconstructionrepresented by the model. The perfor- mance of the algorithm is comparedto existing methods using several numerical examples. In the examplesconsidered, the proposed method demonstrates significant improvementin the quality of reconstruction for the same sample size.