We introduce a new micro-macro Markov chain Monte Carlo method (mM-MCMC) with indirect reconstruction 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. This paper discusses an indirect method to reconstruct microscopic samples from macroscopic reaction coordinate values, that can also be applied in cases where direct reconstruction is cumbersome. The indirect reconstruction method generates a microscopic sample by performing a biased microscopic simulation, starting from the previous microscopic sample and driving the microscopic state towards the proposed reaction coordinate value. We show numerically that the mM-MCMC scheme with indirect reconstruction can significantly extend the range of applicability of the mM-MCMC method.

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使用反应坐标建议的分子动力学微宏马尔可夫链蒙特卡罗方法 II：间接重建

我们引入了一种新的微宏马尔可夫链蒙特卡罗方法 (mM-MCMC)，通过间接重构来采样分子动力学系统的不变分布，这些系统在微观（快速）动力学和宏观（慢速）动力学之间存在时间尺度分离一些低维的反应坐标集。该算法通过允许在宏观层面上进行更大的提议移动，在存在亚稳态的情况下增强了对状态空间的探索，在宏观层面上应用了条件接受 - 拒绝过程。只有当宏观提议被接受时，才从新采样的反应坐标值重建完整的微观状态，并进行第二次接受/拒绝程序。计算收益源于大多数提案在宏观层面被拒绝的事实，以低计算成本，而微观状态一旦重建，几乎总是被接受。本文讨论了一种从宏观反应坐标值重建微观样品的间接方法，该方法也适用于直接重建繁琐的情况。间接重建方法通过执行有偏差的微观模拟来生成微观样本，从先前的微观样本开始并将微观状态推向建议的反应坐标值。我们从数值上表明，具有间接重建的 mM-MCMC 方案可以显着扩展 mM-MCMC 方法的适用范围。本文讨论了一种从宏观反应坐标值重建微观样品的间接方法，该方法也适用于直接重建繁琐的情况。间接重建方法通过执行有偏差的微观模拟来生成微观样本，从先前的微观样本开始并将微观状态推向建议的反应坐标值。我们从数值上表明，具有间接重建的 mM-MCMC 方案可以显着扩展 mM-MCMC 方法的适用范围。本文讨论了一种从宏观反应坐标值重建微观样本的间接方法，该方法也适用于直接重建繁琐的情况。间接重建方法通过执行有偏差的微观模拟来生成微观样本，从先前的微观样本开始并将微观状态推向建议的反应坐标值。我们从数值上表明，具有间接重建的 mM-MCMC 方案可以显着扩展 mM-MCMC 方法的适用范围。从之前的微观样品开始，将微观状态推向建议的反应坐标值。我们从数值上表明，具有间接重建的 mM-MCMC 方案可以显着扩展 mM-MCMC 方法的适用范围。从之前的微观样品开始，将微观状态推向建议的反应坐标值。我们从数值上表明，具有间接重建的 mM-MCMC 方案可以显着扩展 mM-MCMC 方法的适用范围。