报告人：陈青山（Clemson University）

报告题目：The multi-level Monte Carlo method for computing quantities of interest

报告摘要：The Monte Carlo (MC) method is the foundation for most ensemble simulations. It is well known that the MC converges to the theoretical expectation as fast as the inverse of the square root of the number of samples, which is considered slow when the variance is large. To obtain an accurate estimate of the expectation, a large number of simulations have to be carried out, and the total cost for the ensemble simulation grows polynomially in terms of N, where N represents the number of degrees of freedom of the discrete system. The multi-level Monte Carlo (MMC) method, which is essentially a variance reduction method, was first proposed by Giles for stochastic differential equations, and then extended to stochastic partial differential equations by other authors. Through an approach not unlike the multigrid method, the MMC utilizes a hierarchy of grids from high to low resolutions. The total computational cost is reduced to the order of N times the alpha power of log of N, where alpha depends on the dimensions. This talk starts with a brief introduction to the MC and the MMC methods. Challenges in applying the method to long-term climate modelings are highlighted, and workarounds are discussed. The talk concludes with recent numerical results in applying the method to quantify the volume transport of an idealized channel model for the Antarctic Circumpolar Current.

报告时间：2017年5月22日星期一下午 3：30-4：30

报告地点：科技楼南楼702