New hybrid Monte Carlo methods and computing the dominant generalized eigenvalue

In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed.     

面向多智能体博弈的并行蒙特卡洛树搜索算法研究

蒙特卡洛树搜索算法是一种常用的强化学习算法,博弈过程中动态空间的指数级增长是制约该算法学习效率的因素。基于并行方法对蒙特卡洛树搜索算法进行优化,提出基于胜率估值传递的并行蒙特卡洛树搜索算法。改进后的并行博弈搜索策略框架包含一个主进程和多个子进程,其中子进程用于探索,主进程根据子进程传递的胜率估值数据进行决策。结合多智能体博弈平台Pommerman进行实验验证,与传统的蒙特卡罗树搜索算法相比,并行蒙特卡罗树搜索算法有效提高了资源利用率、博弈胜率及决策效率。     

Parallel computing of diatomic molecular rarefied gas flows

A parallel algorithm for direct simulation Monte Carlo calculation of diatomic molecular rarefied gas flows is presented. For reliable simulation of such flow, an efficient molecular collision model is required. Using the molecular dynamics method, the collision of N₂ molecules is simulated. For this molecular dynamics simulation, the parameter decomposition method is applied for parallel computing. By using these results, the statistical collision model of diatomic molecule is constructed. For validation this model is applied to the direct simulation Monte Carlo method to simulate the energy distribution at equilibrium condition and the structure of normal shock wave. For this DSMC calculation, the domain decomposition is applied. It is shown that the collision process of diatomic molecules can be calculated precisely and the parallel algorithm can be efficiently implemented on the parallel computer.     

A parallel algorithm for random walk construction with applicationto the Monte Carlo solution of partial differential equations

Random walks are widely applicable in statistical and scientific computations. In particular, they are used in the Monte Carlo method to solve elliptic and parabolic partial differential equations (PDEs). This method holds several advantages over other methods for PDEs as it solves problems with irregular boundaries and/or discontinuities, gives solutions at individual points, and exhibits great parallelism. However, the generation of each random walk in the Monte Carlo method has been done sequentially because each point in the walk is derived from the preceding point by moving one grid step along a randomly selected direction. A parallel algorithm for random walk generation in regular as well as irregular regions is presented. The algorithm is based on parallel prefix computations. The communication structure of the algorithm is shown to ideally fit on a hypercube of n nodes, where n is the number of processors     

基于混合蒙特卡洛算法的容差分配研究

针对航空制造业中,当容差分配问题中含有装配成功率等随机约束时,常用的数值算法往往难以处理。为提高产品制造精度,提出了混合蒙特卡洛(Hybrid Monte Carlo,HMC)算法,即把动态蒙特卡洛(Dynamic Monte Carlo,DMC)算法和静态蒙特卡罗(SMC)算法结合起来,将DMC用于容差分配的优化仿真运算,把SMC用来处理装配成功率约束。通过仿真验证了该方案的可行性,混合蒙特卡洛法既合理地处理了随机约束,证明装配准确度计算和容差分配的一致性。结果说明求解这类问题是最佳算法。     

Stochastic model for boundary detection

A Markov model is presented for the joint distribution of grey levels and boundary labels in digital images, and perceived as embodying prior expectations about boundary behaviour. The detected boundaries correspond to a local maximum in the conditional distribution over all possible boundary interpretations given the observed intensity image; this is obtained by a highly parallel Monte Carlo algorithm called ‘stochastic relaxation’.     

Condition for relaxed Monte Carlo method of solving systems of linear equations

In this paper, we point out the limitation of the paper entitled “Solving Systems of Linear Equations with Relaxed Monte Carlo Method” published in this journal (Tan in J. Supercomput. 22:113–123, 2002). We argue that the relaxed Monte Carlo method presented in Sect. 7 of the paper is only correct under the condition that the coefficient matrix A must be diagonal dominate. However, for nondiagonal dominate case; the corresponding Neumann series may diverge, which would lead to infinite loop when simulating the iterative Monte Carlo algorithm. In this paper, we first prove that only for the diagonal dominate matrix, the corresponding von Neumann series can converge, and the Monte Carlo algorithm can be relaxed. Therefore, it is not true for nondiagonal dominate matrix, no matter the relaxed parameter γ is a single value or a set of values. We then present and analyze the numerical experiment results to verify our arguments.     

Large-scale reliability-based structural optimization

A robust and efficient methodology is presented for treating large-scale reliability-based structural optimization problems. The optimization is performed with evolution strategies, while the reliability analysis is carried out with the Monte Carlo simulation method incorporating the importance sampling technique to reduce the sample size. Efficient hybrid methods are implemented to solve the reanalysis-type problems that arise in the optimization phase with evolution strategies and in the reliability analysis with Monte Carlo simulations. These hybrid solution methods are based on the preconditioned conjugate gradient algorithm using efficient preconditioning schemes. The numerical tests presented demonstrate the computational advantages of the proposed methods, which become more pronounced for large-scale optimization problems.     

A genetic algorithm based method for bidding strategy coordination in energy and spinning reserve markets

The problem of building optimally coordinated bidding strategies for competitive suppliers in energy and spinning reserve markets is addressed based on the Monte Carlo simulation and a refined genetic algorithm (RGA). It is assumed that each supplier bids a linear energy supply function and a linear spinning reserve supply function into the energy and spinning reserve markets, respectively, and the two markets are dispatched separately to minimize customer payments. Each supplier chooses the coefficients in the linear energy and spinning reserve supply functions to maximize total benefits, subject to expectations about how rival suppliers will bid. A stochastic optimization model is first developed to describe this problem and a Monte Carlo and genetic algorithm based method is then presented to solve it. A numerical example is utilized to illustrate the essential features of the method.     

Monte Carlo implementation of financial simulation on Cell/B.E. multi-core processor

The processor evolution has reached a critical moment in time where it will soon be impossible to increase the frequency much further. Processor designers such as Motorola, Intel and IBM have all realised that the only way to improve the FLOP/Watt ratio is to develop multi-core devices. One of the most current examples of multi-core processors is the new Sony/Toshiba/IBM Cell/B.E. multi-core processor. For the suitability to run in parallel, Monte Carlo methods are often considered embarrassingly parallel. This paper describes how a common Monte Carlo based financial simulation can be calculated in parallel using the Cell/B.E. multi-core processor. The measured performance with the achieved multi-core speed-up is also presented. With the recent availability of this increasingly available technology, financial simulations can now be performed in a fraction of the time it used to. This can also be achieved with a limited power and volume budget using commercially available technology. The main challenge with multi-core devices is clearly the programmability. The work presented here describes how this challenge could be dealt with.A basic MPI library has been developed to handle the partitioning and communication of data. The thread creation follows a POSIX thread creation model. MPI together with POSIX make the application portable in between various multi-processor systems and multi-core devices. The conclusions made indicate that a function offload MPI implementation on the Cell/B.E. multi-core processor can efficiently be used to speed-up the Monte Carlo solution of financial simulations. The conclusions made herein are also applicable to other situations where an algorithm can be easily parallelized.     

Parallel simulation of electron-solid interactions for electron microscopy modeling

A parallel implementation of a Monte Carlo algorithm for modeling the scattering of electrons in solids and the resulting X-ray production is described. Two important issues for accurate and fast parallel simulation are discussed-random number generation and load-balancing. Timing results for the parallel simulation are given which show even modest-sized parallel machines can be competitive with conventional vector supercomputers for Monte Carlo trajectory simulations. Examples of parallel calculations performed to analyze specimen composition data and to characterize electron microscope performance are briefly highlighted.     

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。     

Decentralized control and state estimation of linear time-periodic systems

The main contributions of this article are the design of a decentralized controller and state estimator for linear time-periodic systems with fixed network topologies. The proposed method to tackle both problems consists of reformulating the linear periodic dynamics as a linear time-invariant system by applying a time-lifting technique and designing a discrete-time decentralized controller and state estimator for the time-lifted formulation. The problem of designing the decentralized estimator is formulated as a discrete-time Kalman filter subject to sparsity constraints on the gains. Two different algorithms for the computation of steady-state observer gains are tested and compared. The control problem is posed as a state feedback gain optimization problem over an infinite-horizon quadratic cost, subject to a sparsity constraint on the gains. An equivalent formulation that consists in the optimization of the steady-state solution of a matrix difference equation is presented and an algorithm for the computation of the decentralized gain is detailed. Simulation results for the practical cases of the quadruple-tank process and an extended 40-tank process are presented that illustrate the performance of the proposed solutions, complemented with numerical simulations using the Monte Carlo method.     

参数反演的微分进化蒙特卡洛算法

针对参数反演问题,提出了微分进化蒙特卡洛算法。此方法是在贝叶斯推理的蒙特卡洛算法的基础上融入微分进化思想。与传统的蒙特卡洛算法相比,此方法有效地缩减了迭代次数,提高了反演精度并具有一定的稳定性。     

On the computation and some applications of multivariate isotonic regression

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restrictions for vector valued parameters. A Fortran program for the earlier proposed algorithm for the computation of multivariate isotonic regression is presented. The convergence of the algorithm is studied when the dimension is greater than or equal to five through Monte Carlo simulations. Two different types of numerical examples are given to illustrate the applications of multivariate isotonic regression.     

Systems Simulation Analysis and Optimization of Insurance Business

Problems of computational actuarial mathematics, dynamic financial analysis, and optimization of insurance business and the possibility of their solution by means of parallel computing on graphics accelerators are discussed. The ruin probability and other performance criteria of an insurance company are estimated by the Monte Carlo method. In many cases, it is the only applicable method. Since the ruin probability is small enough, to achieve an acceptable estimate accuracy, an astronomical number of simulations may be required. Parallelization of the Monte Carlo method and the use of graphical accelerators allow us getting the desired result in a reasonable time. The results of numerical experiments on the developed system of actuarial modeling are presented, allowing the use of graphical accelerator that supports Nvidia CUDA 1.3 and higher.     

Parallelization of adaptive MC integrators

Monte Carlo (MC) methods for numerical integration seem to be embarrassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on each processor can potentially ruin the adaptive behaviour. Using the popular VEGAS-Algorithm as an example an economic method of semi-micro parallelization with variable grain-size is presented and contrasted with another straightforward approach of macro-parallelization. A portable implementation of this semi-micro parallelization is used in the xloops-project and is made publicly available.     

Optimization of the Monte Carlo code for modeling of photon migration in tissue

The Monte Carlo method is frequently used to simulate light transport in turbid media because of its simplicity and flexibility, allowing to analyze complicated geometrical structures. Monte Carlo simulations are, however, time consuming because of the necessity to track the paths of individual photons. The time consuming computation is mainly associated with the calculation of the logarithmic and trigonometric functions as well as the generation of pseudo-random numbers. In this paper, the Monte Carlo algorithm was developed and optimized, by approximation of the logarithmic and trigonometric functions. The approximations were based on polynomial and rational functions, and the errors of these approximations are less than 1% of the values of the original functions. The proposed algorithm was verified by simulations of the time-resolved reflectance at several source-detector separations. The results of the calculation using the approximated algorithm were compared with those of the Monte Carlo simulations obtained with an exact computation of the logarithm and trigonometric functions as well as with the solution of the diffusion equation. The errors of the moments of the simulated distributions of times of flight of photons (total number of photons, mean time of flight and variance) are less than 2% for a range of optical properties, typical of living tissues. The proposed approximated algorithm allows to speed up the Monte Carlo simulations by a factor of 4. The developed code can be used on parallel machines, allowing for further acceleration.     

三对角线性方程组的一种有效分布式并行算法

提出了分布式存储环境下求解三对角线性方程的一种并行算法,该算法基于“分而治之”的策略,高效地形成并求解其缩减方程组,避免不必要的冗余计算,通过对计算量的仔细估计,较好地平衡了各处理机的负载;同时,充分利用了计算与通信重叠技术,减少处理机空闲时间,分析了自救的复杂性,给 分布存储多计算机系统上的数值试验结果,数值结果表明,算法的效率较迟利华和李晓梅的ＤＰＰ算法有较大的提高。     

Parallel exact sampling and evaluation of Gaussian Markov random fields

Markov chain Monte Carlo algorithms are computationally expensive for large models. Especially, the so-called one-block Metropolis-Hastings (M-H) algorithm demands large computational resources, and parallel computing seems appealing. A parallel one-block M-H algorithm for latent Gaussian Markov random field (GMRF) models is introduced. Important parts of this algorithm are parallel exact sampling and evaluation of GMRFs. Parallelisation is achieved with parallel algorithms from linear algebra for sparse symmetric positive definite matrices. The parallel GMRF sampler is tested for GMRFs on lattices and irregular graphs, and gives both good speed-up and good scalability. The parallel one-block M-H algorithm is used to make inference for a geostatistical GMRF model with a latent spatial field of 31,500 variables.