A surrogate-based uncertainty quantification with quantifiable errors

Abstract

Surrogate models are often employed to reduce the computational cost required to complete uncertainty quantification, where one is interested in propagating input parameters uncertainties throughout a complex engineering model to estimate responses uncertainties. An improved surrogate construction approach is introduced here which places a premium on reducing the associated computational cost. Unlike existing methods where the surrogate is constructed first, then employed to propagate uncertainties, the new approach combines both sensitivity and uncertainty information to render further reduction in the computational cost. Mathematically, the reduction is described by a range finding algorithm that identifies a subspace in the parameters space, whereby parameters uncertainties orthogonal to the subspace contribute negligible amount to the propagated uncertainties. Moreover, the error resulting from the reduction can be upper-bounded. The new approach is demonstrated using a realistic nuclear assembly model and compared to existing methods in terms of computational cost and accuracy of uncertainties. Although we believe the algorithm is general, it will be applied here for linear-based surrogates and Gaussian parameters uncertainties. The generalization to nonlinear models will be detailed in a separate article. (authors)