This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method...This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method is efficient.展开更多
We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in...We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.展开更多
Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain M...Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.展开更多
采用不同方法对基于热传导反问题的固体热导率预测进行了研究。分别采用Bayesian统计方法、Levenberg-Marquardt和遗传算法对二维各向异性材料的热物性进行了预测,并进行了分析比较。研究结果表明,Bayesian方法中热传导反问题的解是其...采用不同方法对基于热传导反问题的固体热导率预测进行了研究。分别采用Bayesian统计方法、Levenberg-Marquardt和遗传算法对二维各向异性材料的热物性进行了预测,并进行了分析比较。研究结果表明,Bayesian方法中热传导反问题的解是其后验概率密度的数学期望,而后验概率密度函数(PPDF)通过测定的温度进行计算获得,用Markov chain Monte Carlo算法计算后验状态空间以得到未知热导率的统计估计,采用Me-tropolis-Hasting算法进行数据采样构造Markov chain,并截取收敛后的样本进行分析。遗传算法是一种相对较新的用于最优化估计的方法,也可以用于求解反问题。展开更多
基于马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)方法的α稳定分布参数估计具有良好的性能,但不合适的提议函数常导致算法不收敛或混合性能不好。针对提议函数难以选择的问题,提出了一种基于自适应Metropolis算法的非对称α稳...基于马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)方法的α稳定分布参数估计具有良好的性能,但不合适的提议函数常导致算法不收敛或混合性能不好。针对提议函数难以选择的问题,提出了一种基于自适应Metropolis算法的非对称α稳定分布参数估计新方法。该方法利用Markov链的历史信息自动调整提议函数的协方差矩阵,使其不断地逼近目标分布,从而获得更好的估计结果。理论分析和仿真结果表明,此方法不仅能准确地估计出α稳定分布的4个参数,而且具有良好的鲁棒性和灵活性。展开更多
文摘This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method is efficient.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10674016,10875013the Specialized Research Foundation for the Doctoral Program of Higher Education under Grant No.20080027005
文摘We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.
基金the sponsorship of the National Basic Research Program of China (973 Program,2013CB228604,2014CB239201)the National Oil and Gas Major Projects of China (2011ZX05014-001-010HZ,2011ZX05014-001-006-XY570) for their funding of this research
文摘Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.
基金National Natural Science Foundation of China(11161031)Natural Science Foundation of Inner Mongolia(2010MS0116,2009MS0107)Higher School Science and Technology Research Project of Inner Mongolia(NJ10085)~~
文摘采用不同方法对基于热传导反问题的固体热导率预测进行了研究。分别采用Bayesian统计方法、Levenberg-Marquardt和遗传算法对二维各向异性材料的热物性进行了预测,并进行了分析比较。研究结果表明,Bayesian方法中热传导反问题的解是其后验概率密度的数学期望,而后验概率密度函数(PPDF)通过测定的温度进行计算获得,用Markov chain Monte Carlo算法计算后验状态空间以得到未知热导率的统计估计,采用Me-tropolis-Hasting算法进行数据采样构造Markov chain,并截取收敛后的样本进行分析。遗传算法是一种相对较新的用于最优化估计的方法,也可以用于求解反问题。
文摘基于马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)方法的α稳定分布参数估计具有良好的性能,但不合适的提议函数常导致算法不收敛或混合性能不好。针对提议函数难以选择的问题,提出了一种基于自适应Metropolis算法的非对称α稳定分布参数估计新方法。该方法利用Markov链的历史信息自动调整提议函数的协方差矩阵,使其不断地逼近目标分布,从而获得更好的估计结果。理论分析和仿真结果表明,此方法不仅能准确地估计出α稳定分布的4个参数,而且具有良好的鲁棒性和灵活性。
