Global sensitivity analysis using sparse grid interpolation and polynomial chaos

Sparse grid interpolation is widely used to provide good approximations to smooth functions in high dimensions based on relatively few function evaluations. By using an efficient conversion from the interpolating polynomial provided by evaluations on a sparse grid to a representation in terms of orthogonal polynomials (gPC representation), we show how to use these relatively few function evaluations to estimate several types of sensitivity coefficients and to provide estimates on local minima and maxima. First, we provide a good estimate of the variance-based sensitivity coefficients of Sobol’ [1] and then use the gradient of the gPC representation to give good approximations to the derivative-based sensitivity coefficients described by Kucherenko and Sobol’ [2]. Finally, we use the package HOM4PS-2.0 [3] to determine the critical points of the interpolating polynomial and use these to determine the local minima and maxima of this polynomial.