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Rare event sampling is an umbrella term for a group of computer simulation methods intended to selectively sample 'special' regions of the dynamic space of systems which are unlikely to visit those special regions through brute-force simulation. A familiar example of a rare event in this context would be nucleation of a raindrop from over-saturated water vapour: although raindrops form every day, relative to the length and time scales defined by the motion of water molecules in the vapour phase the formation of a liquid droplet is extremely rare. Due to the wide use of computer simulation across very different fields of endeavour, articles on the topic arise from quite disparate sources and it is difficult to make a coherent survey of rare event sampling techniques. Contemporary methods include Transition Path Sampling (TPS),〔 Repetitive Simulation Trials After Reaching Thresholds (RESTART),〔 Forward Flux Sampling (FFS), Generalized Splitting, Adaptive Multilevel Splitting (AMS), Stochastic Process Rare Event Sampling (SPRES) and Subset simulation. The first published rare event technique was by Herman Kahn and Theodore Edward Harris in 1951, who in turn referred to an unpublished technical report by John von Neumann and Stanislaw Ulam. == Generation of Trajectory Fragments == To generate simulation trajectories it is typically necessary to find some way of altering an existing configuration or trajectory so as to explore new regions of the configurational space. A common theme in RESTART, FFS, AMS and SPRES (at least) is the idea of 'splitting' (or 'enrichment'), in which trajectories of a stochastic system are made to diverge by changing the seed of the random number generator. Selectively splitting trajectories allows the simulation to over-sample regions of its dynamical space which are judged in some sense interesting. In order to limit computational cost, trajectories which are judged relatively less interesting (less close to manifesting the target rare event) must be therefore be killed (or 'pruned'). The differences between these splitting algorithms then manifest in the choice of pruning and enrichment approach. While it is often reasonable to introduce randomness to a system which would otherwise be considered deterministic (such as by coupling a microscopic system to a fluctuating heat bath, or by perturbing the velocities in a mesoscopic system after collisions) splitting methods in general sit most comfortably with the study of systems which have a large natural stochastic element in their dynamics. The contrast to splitting methods is provided by TPS, in which 'shooting' is instead typically employed: for a strictly deterministic system, the new path must be created by making a small change to the initial conditions rather than by branching from a point mid-way into the simulation. If the dynamics of a system are chaotic then shooting moves based on perturbation of the start coordinates should have a very high rate of failure in generating rare events, however a benefit is that shooting can function equally well (if time-symmetry is present) by making a perturbation to the final conditions of the system (post rare-event) and running the simulation backwards, thereby sampling new paths with the guarantee that they terminate in the rare event. If the assumptions of equilibrium holding only at the initial (or final) conditions are relaxed, then shooting moves can also be made by perturbing the system during a shot. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「rare event sampling」の詳細全文を読む スポンサード リンク
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