Monte Carlo estimation of sparse grid interpolation residual for stochastic collocation of high-order systems with uncertainties

In fast sampling-based stochastic numerical techniques, Smolyak-based sparse grids are used to construct interpolation of the system output in random domain. The accuracy and convergence of sparse grid interpolations are evaluated by calculating the residual of the interpolation outputs compared with actual output values at grid nodes of higher levels. The residual is used as a criteria for adaptive refinement, as well as local refinement of sparse grids. In this paper, we propose a Monte Carlo sampling-based method to estimate the residual of sparse grid interpolations.