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SP3-coupled global variance reduction method based on RMC code

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Nuclear Science and Techniques 2021年第11期32卷 42-51页

作者： Qing-Quan Pan Teng-Fei Zhang Xiao-Jing Liu Hui He Kan Wang School of Nuclear Science and Engineering Shanghai Jiao Tong UniversityShanghai 200240China Department of Engineering Physics Tsinghua UniversityBeijing 100084Chin

A global variance reduction(GVR)method based on the SPN method is proposed.First,the global multi-group cross-sections are obtained by Monte Carlo(MC)global homogenization.Then,the SP3 equation is solved to obtain the global flux distribution.Finally,the global weight windows are approximated by the global flux distribution,and the GVR simulation is performed.This GVR method is implemented as an automatic process in the RMC code.The SP3-coupled GVR method was tested on a modified version of C5 G7 benchmark with a thickened water shield.The results show that the SP3-coupled GVR method can improve the efficiency of MC criticality calculation.

关键词： RMC code Global homogenization variance reduction SPN theory

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A convergence analysis for a class of practical variance-reduction stochastic gradient MCMC

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Science China(Information Sciences) 2019年第1期62卷 67-79页

作者： Changyou CHEN Wenlin WANG Yizhe ZHANG Qinliang SU Lawrence CARIN Department of Computer Science and Engineering Department of Electrical and Computer Engineering Duke University Microsoft Research School of Data and Computer Science Sun Yat-sen University

Stochastic gradient Markov chain Monte Carlo(SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms. However, there has been little theoretical analysis of the impact of minibatch size to the algorithm’s convergence rate. In this paper, we prove that at the beginning of an SG-MCMC algorithm, i.e., under limited computational budget/time, a larger minibatch size leads to a faster decrease of the mean squared error bound. The reason for this is due to the prominent noise in small minibatches when calculating stochastic gradients, motivating the necessity of variance reduction in SG-MCMC for practical use. By borrowing ideas from stochastic optimization, we propose a simple and practical variance-reduction technique for SG-MCMC, that is efficient in both computation and storage.More importantly, we develop the theory to prove that our algorithm induces a faster convergence rate than standard SG-MCMC. A number of large-scale experiments, ranging from Bayesian learning of logistic regression to deep neural networks, validate the theory and demonstrate the superiority of the proposed variance-reduction SG-MCMC framework.

关键词： Markov chain Monte Carlo SG-MCMC variance reduction deep neural networks

A Distributed Computing Framework Based on Lightweight variance reduction Method to Accelerate Machine Learning Training on Blockchain

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China Communications 2020年第9期17卷 77-89页

作者： Zhen Huang Feng Liu Mingxing Tang Jinyan Qiu Yuxing Peng Science and Technology on Parallel and Distributed Laboratory National University of Defense TechnologyChangsha 410000China H.R.Support Center PLABeijing 100000China

To security support large-scale intelligent applications,distributed machine learning based on blockchain is an intuitive solution scheme.However,the distributed machine learning is difficult to train due to that the corresponding optimization solver algorithms converge slowly,which highly demand on computing and memory resources.To overcome the challenges,we propose a distributed computing framework for L-BFGS optimization algorithm based on variance reduction method,which is a lightweight,few additional cost and parallelized scheme for the model training process.To validate the claims,we have conducted several experiments on multiple classical datasets.Results show that our proposed computing framework can steadily accelerate the training process of solver in either local mode or distributed mode.

关键词： machine learning optimization algorithm blockchain distributed computing variance reduction

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Bayesian autoregressive adaptive refined descriptive sampling algorithm in the Monte Carlo

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Statistical Theory and Related Fields 2023年第3期7卷 177-187页

作者： Djoweyda Ghouil Megdouda Ourbih-Tari Département de Mathématiques Facultédes Sciences ExactesUniversitéde Tizi OuzouTizi OuzouAlgeria Laboratoire deMathématiques appliquées Facultédes Sciences Exactes et InformatiqueUniversitéde JijelJijelAlgeria Institute of Science University Center of TipazaTipazaAlgeria Laboratoire de Mathématiques appliquées Facultédes Sciences ExactesUniversitéde BejaiaBejaiaAlgeria

This paper deals with the Monte Carlo Simulation in a Bayesian framework.It shows the impor-tance of the use of Monte Carlo experiments through refined descriptive sampling within the autoregressive model Xt=ρXt-1+Yt,where 0<ρ<1 and the errors Yt are independent ran-dom variables following an exponential distribution of parameterθ.To achieve this,a Bayesian Autoregressive Adaptive Refined Descriptive Sampling(B2ARDS)algorithm is proposed to esti-mate the parametersρandθof such a model by a Bayesian method.We have used the same prior as the one already used by some authors,and computed their properties when the Nor-mality error assumption is released to an exponential distribution.The results show that B2ARDS algorithm provides accurate and efficient point estimates.

关键词： Monte Carlo simulation reﬁned descriptive sampling methods variance reduction autoregressive process Bayesian estimation

A Branching Random Walk Method for Many-Body Wigner Quantum Dynamics

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 21-71页

作者： Sihong Shao Yunfeng Xiong LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China

A branching random walk algorithm for many-body Wigner equations and its numerical applications for quantum dynamics in phase space are proposed and ana-lyzed in this paper.Using an auxiliary function,the truncated Wigner equation and its adjoint form are cast into integral formulations,which can be then reformulated into renewal-type equations with probabilistic interpretations.We prove that the first mo-ment of a branching random walk is the solution for the adjoint equation.With the help of the additional degree of freedom offered by the auxiliary function,we are able to produce a weighted-particle implementation of the branching random walk.In contrast to existing signed-particle implementations,this weighted-particle one shows a key ca-pacity of variance reduction by increasing the constant auxiliary function and has no time discretization errors.Several canonical numerical experiments on the 2D Gaussian barrier scattering and a 4D Helium-like system validate our theoretical findings,and demonstrate the accuracy,the efficiency,and thus the computability of the proposed weighted-particle Wigner branching random walk algorithm.

关键词： Wigner equation branching random walk quantum dynamics variance reduction signed-particle Monte Carlo method adjoint equation renewal-type equations importance sam-pling resampling

Antithetic Power Transformed Random Variables in Computer Simulations: An Error Correction Mechanism

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Journal of Applied Mathematics and Physics 2023年第6期11卷 1707-1727页

作者： Dennis Ridley Pierre Ngnepieba School of Business & Industry Florida A&M University Tallahassee FL USA Department of Scientific Computing Florida State University Tallahassee FL USA Department of Mathematics Florida A&M University Tallahassee FL USA

A traditional method of Monte Carlo computer simulation is to obtain uniformly distributed random numbers on the interval from zero to one from a linear congruential generator (LCG) or other methods. Random variates can then be obtained by the inverse transformation technique applied to random numbers. The random variates can then be used as input to a computer simulation. A response variable is obtained from the simulation results. The response variable may be biased for various reasons. One reason may be the presence of small traces of serial correlation in the random numbers. The purpose of this paper is to introduce an alternative method of response variable acquisition by a power transformation applied to the response variable. The power transformation produces a new variable that is negatively correlated with the response variable. The response variable is then regressed on its power transformation to convert the units of the power transformed variable back to those of the original response variable. A weighted combination of these two variables gives the final estimate. The combined estimate is shown to have negligible bias. The correlations of various antithetic variates obtained from the power transformation are derived and illustrated to provide insights for this research and for future research into this method.

关键词： Inverse Correlation variance reduction Antithetic Random Variates Simulation Model Bias Bias reduction

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一类非凸优化问题的邻近拟牛顿方法的复杂性

Chinese Quarterly Journal of Mathematics 2023年第1期38卷 62-84页

作者：金玲子 School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Peng Cheng Laboratory Shenzhen 518066China

This paper studies a class of nonconvex composite optimization, whose objective is a summation of an average of nonconvex(weakly) smooth functions and a convex nonsmooth function, where the gradient of the former function has the H o¨lder continuity. By exploring the structure of such kind of problems, we first propose a proximal(quasi-)Newton algorithm wPQN(Proximal quasi-Newton algorithm for weakly smooth optimization) and investigate its theoretical complexities to find an approximate solution. Then we propose a stochastic variant algorithm wPSQN(Proximal stochastic quasi-Newton algorithm for weakly smooth optimization), which allows a random subset of component functions to be used at each iteration. Moreover, motivated by recent success of variance reduction techniques, we propose two variance reduced algorithms,wPSQN-SVRG and wPSQN-SARAH, and investigate their computational complexity separately.

关键词： Nonconvex optimization Nonsmooth optimization Holder continuity Proximal quasi-Newton variance reduction

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On Trajectory Splitting for Accelerating Dynamic Simulations in Mobile Wireless Networks

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On Trajectory Splitting for Accelerating Dynamic Simulations...