论文标题
使用反应坐标提案I：直接重建
A micro-macro Markov chain Monte Carlo method for molecular dynamics using reaction coordinate proposals I: direct reconstruction
论文作者
论文摘要
我们引入了一种新的Micro-Macro Markov链蒙特卡洛法（MM-MCMC），以样本的分子动力学系统的不变分布，该分子表现出显微镜（快速）动力学与宏观（慢速）动力学之间的时间尺度分离的某些低维反应反应均应集的动力学。该算法通过允许在宏观水平上进行更大的建议移动，从而在存在亚稳定性的情况下增强了对状态空间的探索，在该水平上采用条件接受程序。仅当接受宏观建议时，从新的采样反应坐标值重建了完整的微观状态，并进行第二次接受/拒绝程序。计算收益源于以下事实：大多数建议在宏观水平上以低计算成本拒绝，而微观状态（一旦重建）几乎总是被接受。我们通过分析表明收敛性并讨论了所提出算法的收敛速率，并在数值上说明了其在许多标准分子测试案例上的效率。我们还研究了选择不同数值参数对所得MM-MCMC方法效率的影响。
We introduce a new micro-macro Markov chain Monte Carlo method (mM-MCMC) to sample invariant distributions of molecular dynamics systems that exhibit a time-scale separation between the microscopic (fast) dynamics, and the macroscopic (slow) dynamics of some low-dimensional set of reaction coordinates. The algorithm enhances exploration of the state space in the presence of metastability by allowing larger proposal moves at the macroscopic level, on which a conditional accept-reject procedure is applied. Only when the macroscopic proposal is accepted, the full microscopic state is reconstructed from the newly sampled reaction coordinate value and is subjected to a second accept/reject procedure. The computational gain stems from the fact that most proposals are rejected at the macroscopic level, at low computational cost, while microscopic states, once reconstructed, are almost always accepted. We analytically show convergence and discuss the rate of convergence of the proposed algorithm, and numerically illustrate its efficiency on a number of standard molecular test cases. We also investigate the effect of the choice of different numerical parameters on the efficiency of the resulting mM-MCMC method.
