Comparison of Monte Carlo and Quasi Monte Carlo Sampling Methods in High Dimensional Model Representation

A number of new techniques which improve the efficiency of random sampling-high dimensional model representation (RS-HDMR) is presented. Comparison shows that quasi Monte Carlo based HDMR (QRS-HDRM) significantly outperforms RS-HDMR. RS/QRS-HDRM based methods also show faster convergence than the Sobol method for sensitivity indices calculation. Numerical tests prove that the developed methods for choosing optimal orders of polynomials and the number of sampled points are robust and efficient.