蒙特卡罗仿真机及其应用

蒙特卡罗仿真机是通过对随机性问题采用Monte Carlo方法进行计算机仿真，从而得出待解问题的解。为了研究复杂的随机问题，文中提出了基于蒙特卡罗的随机模拟法的蒙特卡罗仿真机，并说明了它的基本原理。通过圆周率的计算，实践了蒙特卡罗仿真机的应用过程，从而显示出蒙特卡罗仿真法处理随机性问题的优越性和仿真普遍的适用性。     

蒙特卡罗与准蒙特卡罗相互融合的整体光照计算

蒙特卡罗方法具备普适性、鲁棒性以及与问题复杂度无关性等优点，非常适于十分难解的整体光照计算问题，但缺点是生成图像随机噪声大．准蒙特卡罗方法计算连续被积函数低维积分的收敛速度快于蒙特卡罗方法，但不适于直接求解复杂的整体光照计算问题．文中研究蒙特卡罗整体光照计算最根本环节，即随机游动的抽样模式，提出融合蒙特卡罗与准蒙特卡罗的两种通用的新型整体光照计算策略．两种新型策略可以应用于所有基于蒙特卡罗的整体光照算法，不仅能够降低生成图像的随机噪声，而且实现简单、不增加计算和存储开销．     

A convergence criterion for the Monte Carlo estimates

In this article, a convergence criterion for the Monte Carlo estimates, which can be used as a stopping rule for the Monte Carlo experiments, will be proposed. The proposed criterion seeks a convergence band of a given width and length such that the probability of the Monte Carlo sample means to fall outside of this band is practically null. Although it has some sort of self defined confidence, equivalent values for the parameters of proposed criterion can be determined through a pilot experiment so as to have a predefined confidence level in the usual statistical sense. Since it does not require sequential computation of the Monte Carlo sample variance, it is computationally more efficient than the usual stopping rule.     

抽象技术及其在蒙特卡洛树搜索中的应用研究综述

抽象技术作为人工智能研究中高效拓展决策的重要组成部分,已广泛应用于大规模的决策问题.蒙特卡洛树搜索虽然在众多决策领域取得了卓越成就,但是在现实决策问题中面临着决策空间巨大和规划周期很长的问题.鉴于此,研究抽象技术及其在蒙特卡洛树搜索中的应用,从状态空间和动作空间两个角度出发分析抽象技术如何提升蒙特卡洛树搜索的决策能力,并对抽象蒙特卡洛树搜索研究中仍需要解决的问题和未来的研究方向作进一步展望.     

Monte Carlo simulation-compatible stochastic field for application to expansion-based stochastic finite element method

In order to endow the expansion-based stochastic formulation with the capability of representing the characteristic behavior of stochastic systems, i.e., the non-linear dependence of the response variability on the coefficient of variation of the stochastic field, a Monte Carlo simulation-compatible stochastic field is suggested. Through a theoretical comparison of displacement vectors in the Monte Carlo method and an expansion-based scheme, it is found that the stochastic field adopted in the expansion-based scheme is not compatible with that appearing in the Monte Carlo simulation. The Monte Carlo simulation-compatible stochastic field is established by means of enforcing the compatibility between the stochastic fields in the expansion-based scheme and the Monte Carlo simulation. Employing the stochastic field suggested in this study, the response variability is reproduced with high precision even for uncertain fields with a moderately large coefficient of variation. Furthermore, the formulation proposed here can be used as an indirect Monte Carlo scheme by directly substituting the numerically simulated random fields into the covariance formula. This yields a pronounced reduction in the computation cost while resulting in virtually the same response variability as the Monte Carlo technique.     

Simulating the Holtsmark distribution by the Monte Carlo method

The Holtsmark distribution is simulated by the Monte Carlo method. Convergence of the Monte Carlo calculation to this distribution is estimated empirically. The problem of the infinite density of energy in the Holtsmark model is considered and ways to solve it are discussed.     

无线传感器网络中移动节点定位算法研究

提出一种利用临时锚节点的蒙特卡罗箱定位算法.该算法是基于蒙特卡罗定位方法之上,通过引入节点平均速率来获取临时锚节点,并利用一跳范围内的临时锚节点构建最小锚盒、增强样本过滤条件,从而加速了采样和样本过滤.此外,在样本的获取上采用了非随机采样的均衡采样方法,有效地降低了采样次数.仿真结果表明:该算法同蒙特卡罗定位算法等相比,提高了节点的定位精度,降低了节点的能耗.     

蒙特卡洛方法在仿真中的应用

本文介绍了蒙特卡洛方法,一种利用随机数(或伪随机数)来解决许多类型计算问题的通用算法。首先描述了蒙特卡洛方法的基本原理,并且通过两个典型应用案例,讨论了蒙特卡洛方法的适用范围和使用条件,展示了该方法的优点,体现了该方法在解决高自由度问题方面的优势。     

基于RMC的蒙特卡罗程序性能优化

蒙特卡罗MC方法是核反应堆设计和分析中重要的粒子输运模拟方法。MC方法能够模拟复杂几何形状且计算结果精度高,缺点是需要耗费大量时间进行上亿规模粒子模拟。如何提高蒙特卡罗程序的性能成为大规模蒙特卡罗数值模拟的挑战。基于堆用蒙特卡罗分析程序RMC,先后开展了基于TCMalloc动态内存分配优化、OpenMP线程调度策略优化、vector内存对齐优化和基于HDF5的并行I/O优化等一系列优化手段,对于200万粒子的算例,使其总体性能提高26.45%以上。     

Methods for uncertainty propagation in life cycle assessment

Life cycle assessment (LCA) calculates the environmental impact of a product over its entire life cycle. Uncertainty analysis is an important aspect in LCA, and is usually performed using Monte Carlo sampling. In this study, Monte Carlo sampling, Latin hypercube sampling, quasi Monte Carlo sampling, analytical uncertainty propagation and fuzzy interval arithmetic were compared based on e.g. convergence rate and output statistics. Each method was tested on three LCA case studies, which differed in size and behaviour. Uncertainty propagation in LCA using a sampling method leads to more (directly) usable information compared to fuzzy interval arithmetic or analytical uncertainty propagation. Latin hypercube and quasi Monte Carlo sampling provide more accuracy in determining the sample mean than Monte Carlo sampling and can even converge faster than Monte Carlo sampling for some of the case studies discussed in this paper.