稀有事件动力学Milestoning方法中首次击中点分布的近似
Approximating First Hitting Point Distribution in Milestoning for Rare Event Kinetics
AI总结：
针对稀有事件动力学Milestoning方法中首次击中点分布无解析解、影响平均首次通过时间精度的问题，提出LPT-M和BI-M两种平衡态近似算法，提升了MFPT精度，还开发了非平衡局部迭代校正算法，计算成本更低。
摘要：
Milestoning（里程碑法）是一种利用短轨迹并行化计算稀有事件动力学的高效方法。平均首次通过时间（MFPT）是Milestoning方法的关键动力学输出，其精度在很大程度上取决于短轨迹系综的初始分布。真实的初始分布，即首次击中点分布（FHPD），在一般情况下不存在解析表达式。本文提出两种算法——局部通过时间加权Milestoning（LPT-M）和贝叶斯推断Milestoning（BI-M），可在平衡条件下准确高效地近似系统的FHPD。我们从里程碑上的玻尔兹曼分布采样出发，计算短轨迹系综的合适权重因子。为进行说明，我们在两个模型示例上测试了这些方法。在MFPT的精度方面，两种方法均比广泛使用的经典Milestoning方法有显著提升。具体而言，在确定性哈密顿动力学中，BI-M将定向Milestoning方法作为一种特例涵盖在内。LPT-M在计算成本和对中间里程碑数量增加的鲁棒性方面尤其具有优势。此外，我们还开发了一种用于非平衡稳态FHPD的局部迭代校正算法，可实现精确的MFPT计算，该算法可与LPT-M/BI-M结合使用，且计算成本远低于精确Milestoning方法。
英文摘要：
Milestoning is an efficient method for rare event kinetics calculation using short trajectory parallelization. Mean first passage time (MFPT) is the key kinetic output of Milestoning, whose accuracy crucially depends the initial distribution of the short trajectory ensemble. The true initial distribution, i.e., first hitting point distribution (FHPD), has no analytic expression in the general case. Here, we introduce two algorithms, local passage time weighted Milestoning (LPT-M) and Bayesian inference Milestoning (BI-M), to accurately and efficiently approximate FHPD for systems at equilibrium condition. Starting from sampling Boltzmann distribution on milestones, we calculate the proper weighting factor for the short trajectory ensemble. The methods are tested on two model examples for illustration purpose. Both methods improve significantly over the widely used classical Milestoning method in terms of the accuracy of MFPT. In particular, BI-M covers the directional Milestoning method as a special case in the deterministic Hamiltonian dynamics. LPT-M is especially advantageous in terms of computational costs and robustness with respect to the increasing number of intermediate milestones. Furthermore, a locally iterative correction algorithm for non-equilibrium stationary FHPD is developed for exact MFPT calculation, which can be combined with LPT-M/BI-M and is much cheaper than the exact Milestoning method.
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