Propagation of uncertainties using improved surrogate models

Abstract

We study the effect of various sources of error on the propagation of uncertain parameters and data through surrogate response surfaces approximating quantities of interest from stochastic differential equations. The main result centers on a novel approach for improving the pointwise accuracy of a surrogate with the use of an adjoint-based a posteriori estimate of its error. A general error analysis on propagated distribution functions for both forward and inverse problems is derived. To provide concrete examples focusing on the use of the improved surrogate, we consider standard polynomial spectral methods to approximate the surrogate. However, neither the definition of the improved surrogate nor the general error analysis for the computed distribution functions requires a specific surrogate formulation. Numerical results comparing pointwise errors in propagated distributions using a surrogate versus its improved counterpart demonstrate global decreases in both actual error and in error bounds for both forward and inverse problems.