The aim of this study is to evaluate the performance of multilevel Monte Carlo (MLMC) sampling technique for uncertainty quantification in stochastic multiscale systems. Two systems, a chemical vapor deposition chamber and a catalytic flow reactor, subject to multiple parameter uncertainty, were considered. The distributions of the systems' observables were estimated using standard MC sampling and polynomial chaos expansions (PCE), where the coefficients were calculated by nonintrusive spectral projection. The MLMC technique was used to efficiently sample the two systems and accurately estimate the data necessary for constructing the PCE expressions. The results show that the usage of MLMC improved the precision of identification of PCE versus the traditional heuristic approach and lowered the computational cost of uncertainty quantification compared to standard MC.

中文翻译：

---

多级蒙特卡罗方法应用于随机多尺度系统的不确定性量化

这项研究的目的是评估用于随机多尺度系统中不确定性量化的多级蒙特卡洛（MLMC）采样技术的性能。考虑了两个系统，一个化学气相沉积室和一个催化流反应器，它们受到多参数不确定性的影响。使用标准MC采样和多项式混沌扩展（PCE）估算系统的可观测值的分布，其中系数是通过非侵入式频谱投影计算的。MLMC技术用于高效采样这两个系统，并准确估计构建PCE表达式所需的数据。