GPU-based simulation of the long-range Potts model via parallel tempering

We discuss the efficiency of parallelization on graphical processing units (GPUs) for the simulation of the one-dimensional Potts model with long-range interactions via parallel tempering. We investigate the behavior of some thermodynamic properties, such as equilibrium energy and magnetization, critical temperatures as well as the separation between the first- and second-order regimes. By implementing multispin coding techniques and an efficient parallelization of the interaction energy computation among threads, the GPU-accelerated approach reached speedup factors of up to 37.     

Global multipath Monte Carlo algorithms for radiosity

We present a new algorithm for radiosity, which is linear both in time and storage with the number of patches in a given scene; that is, the number of patches is increased by dividing each existing patch into smaller patches. The new algorithm is based on Integral Geometry and on the well-known algorithms for Monte Carlo particle transport. It considers the scene embedded in a field of lines, each representing the exchange between the pairs of points that result from the intersections of the line with the scene. For a given pair of points, this exchange is bidirectional. Lines are taken randomly. Both graphical and numerical results are given for the proposed algorithm, which is compared with a local Monte Carlo particle transport algorithm.     

Stochastic kinetic Monte Carlo algorithms for long-range Hamiltonians

We present a higher order kinetic Monte Carlo methodology suitable to model the evolution of systems in which the transition rates are non-trivial to calculate or in which Monte Carlo moves are likely to be non-productive flicker events. The second order residence time algorithm first introduced by Athènes et al. [Phil. Mag. A 76 (1997) 565] is rederived from the n-fold way algorithm of Bortz et al. [J. Comput. Phys. 17 (1975) 10] as a fully stochastic algorithm. The second order algorithm can be dynamically called when necessary to eliminate unproductive flickering between a metastable state and its neighbours. An algorithm combining elements of the first order and second order methods is shown to be more efficient, in terms of the number of rate calculations, than the first order or second order methods alone while remaining statistically identical. This efficiency is of prime importance when dealing with computationally expensive rate functions such as those arising from long-range Hamiltonians. Our algorithm has been developed for use when considering simulations of vacancy diffusion under the influence of elastic stress fields. We demonstrate the improved efficiency of the method over that of the n-fold way in simulations of vacancy diffusion in alloys. Our algorithm is seen to be an order of magnitude more efficient than the n-fold way in these simulations. We show that when magnesium is added to an Al-2at.%Cu alloy, this has the effect of trapping vacancies. When trapping occurs, we see that our algorithm performs thousands of events for each rate calculation performed.     

QSAR/QSPR模型中的蒙特卡罗交叉效验评价

介绍了用于QSAR或QSPR模型的蒙特卡罗(Monte Carlo)交叉效验模型评价方法。该方法是采用蒙特卡罗随机思想把数据集随机的分成训练集和预测集来对模型进行交叉效验,从模型的预测能力和预测稳定性两个方面评价模型。通过研究不同代表性的3套化学数据的结果表明,与k-折交叉效验相比,Monte Carlo交叉效验,是一种有效且稳定的QSAR或QSPR模型的评价方法。     

Monte Carlo algorithms for evaluating Sobol’ sensitivity indices

Sensitivity analysis is a powerful technique used to determine robustness, reliability and efficiency of a model. The main problem in this procedure is the evaluating total sensitivity indices that measure a parameter’s main effect and all the interactions involving that parameter. From a mathematical point of view this problem is presented by a set of multidimensional integrals. In this work a simple adaptive Monte Carlo technique for evaluating Sobol’ sensitivity indices is developed. A comparison of accuracy and complexity of plain Monte Carlo and adaptive Monte Carlo algorithms is presented. Numerical experiments for evaluating integrals of different dimensions are performed.     

An optimized algorithm for ionized impurity scattering in Monte Carlo simulations

We present a new optimized model of Brookes-Herring ionized impurity scattering for use in Monte Carlo simulations of semiconductors. When implemented, it greatly decreases the execution time needed for simulations (typically by a factor of the order of 100), and also properly incorporates the great proportion of small angle scatterings that are neglected in the standard algorithm. It achieves this performance by using an anisotropic choice of scattering angle which accurately mimics the true angular distribution of ionized impurity scattering.     

Performance modeling using Monte Carlo simulation

Cycle accurate simulation has long been the primary tool for micro-architecture design and evaluation. Though accurate, the slow speed often imposes constraints on the extent of design exploration. In this work, we propose a fast, accurate Monte-Carlo based model for predicting processor performance. We apply this technique to predict the CPI of in-order architectures and validate it against the Itanium-2. The Monte Carlo model uses micro-architecture independent application characteristics, and cache, branch predictor statistics to predict CPI with an average error of less than 7%. Since prediction is achieved in a few seconds, the model can be used for fast design space exploration that can efficiently cull the space for cycle-accurate simulations. Besides accurately predicting CPI, the model also breaks down CPI into various components, where each component quantifies the effect of a particular stall condition (branch misprediction, cache miss, etc.) on overall CPI. Such a CPI decomposition can help processor designers quickly identify and resolve critical performance bottlenecks.     

Application of new Monte Carlo algorithms to random spin systems

We explain the idea of the probability-changing cluster (PCC) algorithm, which is an extended version of the Swendsen-Wang algorithm. With this algorithm, we can tune the critical point automatically. We show the effectiveness of the PCC algorithm for the case of the three-dimensional (3D) Ising model. We also apply this new algorithm to the study of the 3D diluted Ising model. Since we tune the critical point of each random sample automatically with the PCC algorithm, we can investigate the sample-dependent critical temperature and the sample average of physical quantities at each critical temperature, systematically. We have also applied another newly proposed algorithm, the Wang-Landau algorithm, to the study of the spin glass problem.     

A reliability-based optimization method using sequential surrogate model and Monte Carlo simulation

This paper presents a sequential surrogate model method for reliability-based optimization (SSRBO), which aims to reduce the number of the expensive black-box function calls in reliability-based optimization. The proposed method consists of three key steps. First, the initial samples are selected to construct radial basis function surrogate models for the objective and constraint functions, respectively. Second, by solving a series of special optimization problems in terms of the surrogate models, local samples are identified and added in the vicinity of the current optimal point to refine the surrogate models. Third, by solving the optimization problem with the shifted constraints, the current optimal point is obtained. Then, at the current optimal point, the Monte Carlo simulation based on the surrogate models is carried out to obtain the cumulative distribution functions (CDFs) of the constraints. The CDFs and target reliabilities are used to update the offsets of the constraints for the next iteration. Therefore, the original problem is decomposed to serial cheap surrogate-based deterministic problems and Monte Carlo simulations. Several examples are adopted to verify SSRBO. The results show that the number of the expensive black-box function calls is reduced exponentially without losing of precision compared to the alternative methods, which illustrates the efficiency and accuracy of the proposed method.

     

Geometrical Monte Carlo model of liquid-phase sintering

Liquid-phase sintering (LPS) is an industrial process used to consolidate materials composed of two different kinds of metallic and/or ceramic powders. At constant temperature, the amount of the present liquid-phase is constant. However, the shape of particles of solid phase changes over time. In general, the rounding of particles and the growth of big particles at the expense of the small ones are observed. This process is known as Ostwald ripening.     

A research of Monte Carlo optimized neural network for electricity load forecast

In this paper, we apply the Monte Carlo neural network (MCNN), a type of neural network optimized by Monte Carlo algorithm, to electricity load forecast. Meanwhile, deep MCNNs with one, two and three hidden layers are designed. Results have demonstrated that three-layer MCNN improves 70.35% accuracy for 7-week electricity load forecast, compared with traditional neural network. And five-layer MCNN improves 17.24% accuracy for 7-week forecast. This proves that MCNN has great potential in electricity load forecast.

     

Discrete range clustering using Monte Carlo methods

For automatic obstacle avoidance guidance during rotorcraft low altitude flight a reliable model of the nearby environment is needed. Such a model may be constructed by applying surface fitting techniques to the dense range map obtained by active sensing using radars. However, for covertness passive sensing techniques using electro-optic sensors is desirable. As opposed to the dense range map obtained via active sensing, passive sensing algorithms produce reliable range at sparse locations and, therefore, surface fitting techniques to fill the gaps in the range measurement are not directly applicable. Both, for automatic guidance and as a display for aiding the pilot, these discrete ranges need to be grouped into sets which correspond to objects in the nearby environment. The focus of this paper is on using Monte Carlo methods for clustering range points into meaningful groups. We compare three different approaches and present results of application of these algorithms to an image sequence acquired by onboard cameras during a helicopter flight. Starting with an initial grouping, these algorithms are iteratively applied with a new group creation algorithm to determine the optimal number of groups and the optimal group membership. The results indicate that the simulated annealing methods do not offer any significant advantage over the basic Monte Carlo method for this discrete optimization problem     

基于Monte Carlo的无线传感器网络定位算法

无线传感器网络节点自身定位技术是无线传感器网络关键技术之一。针对目前各种定位算法存在定位精度较低的问题,提出了一种基于Monte Carlo方法的定位算法,该算法利用粒子到锚节点的距离计算各粒子的权值,通过滤波不断更新粒子的集合,使粒子收敛到未知节点的位置。对非视线情况、不同锚节点个数、迭代次数及粒子数进行了定位过程仿真,并和极大似然估计定位算法进行了定位结果比较。结果表明:该算法充分利用了对节点位置估计的有效信息,一定程度上抑制了非视线误差的影响,定位精度高,稳定性好。     

极性电介质极化规律的蒙特卡罗模拟研究

使用蒙特卡罗方法模拟了极性电介质的极化现象,结果显示:系统达到平衡态后,倾向于电场方向的分子数增多,逆着电场方向的分子数减少,每个分子电矩的取向仍不断发生变化;电场越强,沿电场方向的分子数越多,电极化强度越大,电极化强度与场强成线性关系;场强不变时,温度越高,分子电矩取向越杂乱,电极化强度越小,说明电介质的极化率和介电常量随温度升高而减小。我们还对20℃、1 atm条件下CH₃Cl、HBr、HCl、CH₃Br、CH₃I、CH₃F、C₂H₅Cl、C₂H₃Cl 8种气体的相对介电常量作了估算,估算值和相应的实验值符合得较好,说明本文的模拟方法可较好地用来估算电介质气体的相对介电常量。     

MontePython: Implementing Quantum Monte Carlo using Python

We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and diffusion Monte Carlo and we describe how to implement theses methods in pure C++ and C++/Python. Furthermore we check the efficiency of the implementations in serial and parallel cases to show that the overhead using Python can be negligible.

Program summary

Program title: MontePythonCatalogue identifier: ADZP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 49 519No. of bytes in distributed program, including test data, etc.: 114 484Distribution format: tar.gzProgramming language: C++, PythonComputer: PC, IBM RS6000/320, HP, ALPHAOperating system: LINUXHas the code been vectorised or parallelized?: Yes, parallelized with MPINumber of processors used: 1-96RAM: Depends on physical system to be simulatedClassification: 7.6; 16.1Nature of problem: Investigating ab initio quantum mechanical systems, specifically Bose-Einstein condensation in dilute gases of ⁸⁷RbSolution method: Quantum Monte CarloRunning time: 225 min with 20 particles (with 4800 walkers moved in 1750 time steps) on 1 AMD Opteron^TM Processor 2218 processor; Production run for, e.g., 200 particles takes around 24 hours on 32 such processors.     

Stochastic DAG scheduling using a Monte Carlo approach

In heterogeneous computing systems, there is a need for solutions that can cope with the unavoidable uncertainty in individual task execution times, when scheduling DAGs. When such uncertainties occur, static DAG scheduling approaches may suffer, and some rescheduling may be necessary. Assuming that the uncertainty in task execution times is modelled in a stochastic manner, we may be able to use this information to improve static DAG scheduling considerably. In this paper, a novel DAG scheduling approach is proposed to solve this stochastic scheduling problem, based on a Monte Carlo method. The approach is built on the top of a classic static DAG scheduling heuristic and evaluated through extensive simulation. Empirical results show that a significant improvement of average application performance can be achieved by the proposed approach at a reasonable execution time cost.     

Video scene segmentation using Markov chain Monte Carlo

Videos are composed of many shots that are caused by different camera operations, e.g., on/off operations and switching between cameras. One important goal in video analysis is to group the shots into temporal scenes, such that all the shots in a single scene are related to the same subject, which could be a particular physical setting, an ongoing action or a theme. In this paper, we present a general framework for temporal scene segmentation in various video domains. The proposed method is formulated in a statistical fashion and uses the Markov chain Monte Carlo (MCMC) technique to determine the boundaries between video scenes. In this approach, a set of arbitrary scene boundaries are initialized at random locations and are automatically updated using two types of updates: diffusion and jumps. Diffusion is the process of updating the boundaries between adjacent scenes. Jumps consist of two reversible operations: the merging of two scenes and the splitting of an existing scene. The posterior probability of the target distribution of the number of scenes and their corresponding boundary locations is computed based on the model priors and the data likelihood. The updates of the model parameters are controlled by the hypothesis ratio test in the MCMC process, and the samples are collected to generate the final scene boundaries. The major advantage of the proposed framework is two-fold: 1) it is able to find the weak boundaries as well as the strong boundaries, i.e., it does not rely on the fixed threshold; 2) it can be applied to different video domains. We have tested the proposed method on two video domains: home videos and feature films, and accurate results have been obtained.     

SISAM and MIXIN: Two algorithms for the computation of posterior moments and densities using Monte Carlo integration

Two algorithms, and corresponding Fortran computer programs, for the computation of posterior moments and densities using the principle of importance sampling are described in detail. The first algorithm makes use of a multivariate Student t importance function as approximation of the posterior. It can be applied when the integrand is moderately skew. The second algorithm makes use of a decomposition: a multivariate normal importance function is used to generate directions (lines) and one-dimensional classical quadrature is used to evaluate the integrals defined on the generated lines. The second algorithm can be used in cases where the integrand is possibly very skew in any direction.