We study the numerical properties of a recently introduced micro-macro Markov chain Monte Carlo (mM-MCMC) scheme that accelerates sampling of Gibbs distributions when there is a time-scale separation between the complete (microscopic) molecular dynamics and the slow dynamics of a low dimensional reaction coordinate. The micro-macro Markov chain works in three steps: 1) compute the reaction coordinate value associated to the current molecular state; 2) generate a new macroscopic proposal using a proposal distribution; 3) reconstruct a molecular configuration that is consistent with the newly sampled macroscopic value. Here, we systematically study the impact of method parameters on the efficiency of the micro-macro Markov chain Monte Carlo method, namely the chosen macroscopic dynamics and the microscopic reconstruction distribution. We specifically investigate the impact of the macroscopic and reconstruction proposal distributions and their parameters on this efficiency on two prototypical molecular systems, a three-atom molecule and butane. We find, through detailed computational experiments, that the efficiency is largest when these proposal distributions are close to their time-invariant counterparts and that it is robust with respect to parameter changes.

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分子动力学微观-宏观马尔可夫链蒙特卡罗方法的计算效率研究

我们研究了最近引入的微观-宏观马尔可夫链蒙特卡罗 (mM-MCMC) 方案的数值特性，当完整的（微观）分子动力学与缓慢的动力学之间存在时间尺度分离时，该方案可加速吉布斯分布的采样。低维反应坐标。微观-宏观马尔可夫链分三步工作：1）计算与当前分子状态相关的反应坐标值； 2）使用提案分布生成新的宏观提案； 3）重建与新采样的宏观值一致的分子构型。在这里，我们系统地研究了方法参数对微观-宏观马尔可夫链蒙特卡罗方法效率的影响，即所选的宏观动力学和微观重构分布。我们专门研究了宏观和重构提议分布及其参数对两个原型分子系统（三原子分子和丁烷）效率的影响。通过详细的计算实验，我们发现，当这些提案分布接近其时不变对应分布时，效率最大，并且对于参数变化具有鲁棒性。