Quasi-Monte Carlo and RBF metamodeling for quantile estimation in river bed morphodynamics

Four generic methods for quantile estimation have been compared: Monte Carlo (MC), Monte Carlo with Harrel-Davis weighting (WMC), quasi- Monte Carlo with Sobol sequence (QMC) and quasi-random splines (QRS). The methods are combined with RBF metamodel and applied to the analysis of morphodynamic hydrodynamic simulations of the river bed evolution. The following results have been obtained. Harrel-Davis weighting gives a moderate 1020 % improvement of precision at small number of samples N ~ 100. Quasi-Monte Carlo methods provide significant improvement of quantile precision, e.g. the number of function evaluations necessary to achieve rms ~ 104 precision is reduced from 1,000,000 for MC to 100,000 for QMC and to 6,000 for QRS. On the other hand, RBF metamodeling of bulky data allows to speed up the computation of one complete result in the considered problem from 45 min (on 32CPU) to 20 s (on 1CPU), providing rapid quantile estimation for the whole set of bulky data.