Uncertainty Quantification of Nuclear Engineering Models: Orthogonal Basis for Polynomial Regression with Derivative Information

We discuss the choice of polynomial basis for approximation of uncertainty propagation through complex simulation models with capability to output derivative information. Our work is a part of larger research effort in uncertainty quantification using sampling methods augmented with derivative information. The approach is distinct from standard polynomial regression, and requires a different setup for best results. In this study, we address orthogonality of the multivariate basis that is used in regression with derivative information. We use a simplified model of heat transport in the nuclear reactor core with uncertainties in material properties as a case study. In our numerical experiments, we compare a new basis, constructed to satisfy the correct orthogonality conditions with such standard choices as Hermite or Lagrange polynomials. The orthogonal basis results in a better numerical conditioning of the regression procedure, a modest improvement in approximation error when basis polynomials are chosen a priori, and a significant improvement when basis polynomials are chosen adaptively, using a stepwise fitting procedure.

Our work can be viewed as a study in the basis choice for sampling-based polynomial regression in the cases when the sampled training data is presented in a non-standard format (in a distributed form, under some parametrization or mapping, augmented with additional information). In that context, our results have long-term significance for the tasks of uncertainty quantification of a wide class of simulation models.

Event Topic:

Computational Mathematics & Statistics