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上海交通大学自然科学研究院最新成果:基于多正则蒙特卡洛算法的不确定性量化方法

近期,上海交通大学自然科学研究院及数学科学学院特别研究员李敬来课题组在国际学术期刊计算物理杂志 ( Journal of Computational Physics)上发表了题为“A surrogate accelerated Multicanonical Monte Carlo method for uncertainty quantification”的论文,报道了他们关于使用多正则蒙特卡洛方法(Multicanonical Monte Carlo)对工程系统中的不确定性进行量化的工作。

几乎所有现实世界中的工程系统都会受到各种随机因素的影响,而研究这些随机因素对系统性能及可靠性对影响是 诸多工程应用中里至关重要的问题,也是所谓不确定性量化(uncertainty quantification)领域的核心问题之一。本文借鉴了统计物理中的多正则蒙特卡洛(MMC)方法,设计了基于MMC的仿真方法来计算随机因素对系统性能造成对影响。另外,为了进一步提高计算效率,本文设计了基于高斯过程回归构的替代模型来对MMC仿真进行加速。数值试验证明,与常规蒙特卡洛方法相比,该方法能够在仿真效率上有几个数量级对提高。

本论文的第一作者吴可奕为致远学院数学方向学生(目前已经毕业并赴美国德州大学奥斯丁分校攻读博士学位)。

参考文献:Keyi Wu, Jinglai Li, “A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification”, Journal of Computational Physics, Volume 321, 15 September 2016, Pages 1098-1109

Abstract: In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter y. The performance parameter y is random due to the presence of various sources of uncertainty in the system, and our goal is to estimate the probability density function (PDF) of y. We propose to use the multicanonical Monte Carlo (MMC) method, a special type of adaptive importance sampling algorithms, to compute the PDF of interest. Moreover, we develop an adaptive algorithm to construct local Gaussian process surrogates to further accelerate the MMC iterations. With numerical examples we demonstrate that the proposed method can achieve several orders of magnitudes of speedup over the standard Monte Carlo methods.