Polynomial regression approaches using derivative information for uncertainty quantification

In this work we describe a polynomial regression approach that uses derivative information for analyzing the performance of a complex system that is described by a mathematical model depending on several stochastic parameters. We construct a surrogate model as a goal-oriented projection onto an incomplete space of polynomials; find coordinates of the projection by regression; and use derivative information to significantly reduce the number of the sample points required to obtain a good model. The simplified model can be used as a control variate to significantly reduce the sample variance of the estimate of the goal. For our test model, we take a steady-state description of heat distribution in the core of the nuclear reactor core, and as our goal we take the maximum centerline temperature in a fuel pin. For this case, the resulting surrogate model is substantially more computationally efficient than random sampling or approaches that do not use derivative information, and it has greater precision than linear models.