A comparison of efficient uncertainty quantification techniques for stochastic multiscale systems

Abstract

The aim of this article is to compare the performance of efficient uncertainty propagation techniques (Polynomial Chaos [PCE] and Power Series [PSE] expansions) for uncertainty quantification in multiscale systems where discrete (molecular) scale is modeled without closed‐form expressions. A multiscale model of thin film formation by chemical vapor deposition was used to study the effects of single parameter and multivariate uncertainty. For the single parameter uncertainty, 2nd order PSE approximations were the most accurate and computationally attractive. For the multivariate uncertainty, PSE performance deteriorated, while 2nd order PCE provided the highest accuracy when its expansion coefficients were calculated using the Least Squares method. However, comparable accuracy was achieved at half the computational cost when the coefficients were calculated using Nonintrusive Spectral Projection (NISP). The response variables were subsequently controlled using robust optimization, and the results obtained using PCE NISP satisfied the optimization constraints more closely than other methods. © 2017 American Institute of Chemical Engineers AIChE J , 63: 3361–3373, 2017