Improving dynamical properties of metropolized discretizations of overdamped Langevin dynamics
Improving dynamical properties of metropolized discretizations of overdamped Langevin dynamics
复制标题
改进过阻尼 Langevin 动力学的都市化离散化的动力学特性
作者：
M. Fathi;G. Stoltz
通过诸如Euler-Maruyama方法之类的方案，过阻尼朗之万动力学的离散化可以通过某种接受/拒绝规则来修正，例如基于Metropolis-Hastings准则。在这种情况下，马尔可夫链采样的不变度量正好是Boltzmann-Gibbs度量。然而，拒绝扰乱了所得到的数值方法与参考动力学的动力学一致性。本文用Metropolis-Hastings方法对紧致空间上过阻尼朗之万动力学离散化的标准修正进行了修正，使我们可以改进数值方法的强阶，或者减少描述动力学有效动力学行为的输运系数估计的偏差。对于后一种方法，我们依赖于修改的数值格式以及接受/拒绝标准的Barker规则。
The discretization of overdamped Langevin dynamics, through schemes such as the Euler-Maruyama method, can be corrected by some acceptance/rejection rule, based on a Metropolis-Hastings criterion for instance. In this case, the invariant measure sampled by the Markov chain is exactly the Boltzmann–Gibbs measure. However, rejections perturb the dynamical consistency of the resulting numerical method with the reference dynamics. We present in this work some modifications of the standard correction of discretizations of overdamped Langevin dynamics on compact spaces by a Metropolis-Hastings procedure, which allow us to either improve the strong order of the numerical method, or to decrease the bias in the estimation of transport coefficients characterizing the effective dynamical behavior of the dynamics. For the latter approach, we rely on modified numerical schemes together with a Barker rule for the acceptance/rejection criterion.
MALA算法的非渐近混合
DOI：
10.48550/arxiv.1008.3514
发表时间：
2010
期刊：
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影响因子：
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作者：
Bou-Rabee N
通讯作者：
Bou-Rabee N