A Polynomial Chaos Approach for Nuclear Data Uncertainties Evaluations

Our interest is particularly targeted towards an uncertainties propagation study for nuclear models. In order to quantify the respective effects of input random coefficients on the calculated cross sections, we use a polynomial chaos expansion to model the propagation of input uncertainties. A nonintrusive regression-based approach is proposed to allow us to compute the Sobol indexes giving the relative importance of each parameter (or any combination of them). The stochastic input is spectrally represented by orthogonal polynomial functionals from the Askey scheme as a trial basis to represent the random space. Two different kinds of orthogonal polynomials from the Askey scheme (Legendre and Hermite polynomials) are used as bases in the random space. Their efficiency and convergence are studied in comparison with numerical solutions obtained by Monte Carlo simulations. It is also shown that the Quasi Monte Carlo method promises a substantial speed-up compared with the classical Monte Carlo method.