Dinner Aaron R, Mattingly Jonathan C, Tempkin Jeremy O B, Van Koten Brian, Weare Jonathan
James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.
SIAM Rev Soc Ind Appl Math. 2018;60(4):909-938. doi: 10.1137/16M1104329. Epub 2018 Nov 8.
We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of state space (strata), computing averages over the distributions of the trajectory fragments within the strata with minimal communication between them, and combining those averages with appropriate weights to yield averages with respect to the original underlying process. Our framework reveals the full generality and flexibility of trajectory stratification, and it illuminates a common mathematical structure shared by existing algorithms for sampling rare events. We demonstrate the power of the framework by defining strata in terms of both points in time and path-dependent variables for efficiently estimating averages that were not previously tractable.
我们提出了一个用于模拟罕见事件的轨迹分层的通用数学框架。轨迹分层包括将基础过程的轨迹分解为限于状态空间受限区域（层）的片段，在这些层内的轨迹片段分布上计算平均值，且它们之间的通信最少，并将这些平均值与适当的权重相结合，以得出关于原始基础过程的平均值。我们的框架揭示了轨迹分层的全面通用性和灵活性，并且阐明了用于对罕见事件进行采样的现有算法所共有的一种通用数学结构。我们通过根据时间点和路径相关变量来定义层，以有效估计以前难以处理的平均值，从而展示了该框架的强大功能。
