Physical processes in the core of a nuclear reactor are modeled by a system of partial differential-algebraic equations with uncertainty. The associated problems of uncertainty quantification may be solved through the creation of a valid simplified version of the system. In our work we describe an approach based on stochastic finite element methods.

We construct a simplified model as a goal-oriented projection onto an incomplete space of interpolating polynomials; find coordinates of the projection by collocation; and use derivative information to significantly reduce the number of the required collocation sample points. The resulting surrogate model is more computationally efficient than random sampling or generic high-order polynomial interpolations, and has greater precision than linear models.

The results of our work transfer to quantifying the uncertainty in hydraulic and neutron interaction processes in the nuclear reactor, and, further, to a wide class of problems of factor analysis, optimization and control.