论文标题
通过重要性采样确定的二维速度场中稀有轨迹的来源和水槽
Sources and Sinks of Rare Trajectories in 2-Dimensional Velocity Fields Identified by Importance Sampling
论文作者
论文摘要
我们以重新定义的方式使用重要性采样，以突出显示和研究稀有事件，以捕获目标相干集中的轨迹的形式。我们采用转移操作员的方法，以通过可移植大学大气模型提供的风速场重建大气的重建二维流动。在极端价值理论的推动下，我们考虑了可观察到的$ ϕ（x）= - \ log（d（x，γ））$在所选目标相干集的中心$γ$上最大化，在这种情况下很少有粒子过渡。我们说明，最大化这种可观察到的重要性采样提供了丰富的数据集，这些轨迹经历了如此罕见的事件。这些轨迹的向后重建提供了有关初始条件的有价值信息，并且很可能会采用轨迹。有了这些信息，与标准集成技术相比，我们能够获得更准确的稀有过渡概率估计值。
We use importance sampling in a redefined way to highlight and investigate rare events in the form of trajectories trapped inside a target coherent set. We take a transfer operator approach to finding these sets on a reconstructed 2-dimensional flow of the atmosphere from wind velocity fields provided by the Portable University Model of the Atmosphere. Motivated by extreme value theory, we consider an observable $ϕ(x) = -\log(d(x,γ))$ maximized at the center $γ$ of a chosen target coherent set, where it is rare for a particle to transition. We illustrate that importance sampling maximizing this observable provides an enriched data set of trajectories that experience such a rare event. Backwards reconstruction of these trajectories provides valuable information on initial conditions and most likely paths a trajectory will take. With this information, we are able to obtain more accurate estimates of rare transition probabilities compared to those of standard integration techniques.
