Uncertainty quantification in nuclear criticality modelling using a high dimensional model representation

An adaptive high dimensional model representation (HDMR) is used to decompose the response parameter keff into a superposition of lower dimensional subspaces which are in-turn projected on to a polynomial basis. These projections are evaluated using an adaptive quadrature scheme which is used to infer the polynomial orders of the basis. The combination of adaptive HDMR and adaptive quadrature techniques results in a sparse polynomial expansion which has been optimised to represent the variance of the response with the minimum number of polynomials. The combined application of these techniques is illustrated using UOX and MOX pin cell problems with evaluated nuclear covariance data. We show that this approach to calculating the variance in keff is an order of magnitude more efficient when compared to Latin Hypercube sampling with the same number of samples for problems involving up to 988 random dimensions.