论文标题
部分可观测时空混沌系统的无模型预测
A Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation
论文作者
论文摘要
我们开发了一种有偏见的蒙特卡洛算法，以测量用于任意碰撞核群聚集聚合中罕见事件的概率。给定具有固定数量碰撞的轨迹，该算法使用局部移动修改了碰撞之间的等待时间以及碰撞的顺序。我们通过提供一种将任意轨迹转换为使用有效的Monte Carlo移动的标准轨迹的协议，证明该算法是千古化的。该算法可以以$ 10^{ - 40} $的订单和较低的订单概率采样罕见事件。算法在采样低概率事件中的有效性是通过证明恒定内核聚集的较大偏差函数的数值结果重现确切结果来确定的。结果表明，算法可以为包括胶凝的核以及非典型时代的插入轨迹获得其他核的较大偏差函数。还表征了算法的不同参数的自相关时间的依赖性。
We develop a biased Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels. Given a trajectory with a fixed number of collisions, the algorithm modifies both the waiting times between collisions, as well as the sequence of collisions, using local moves. We show that the algorithm is ergodic by giving a protocol that transforms an arbitrary trajectory to a standard trajectory using valid Monte Carlo moves. The algorithm can sample rare events with probabilities of the order of $10^{-40}$ and lower. The algorithm's effectiveness in sampling low-probability events is established by showing that the numerical results for the large deviation function of constant-kernel aggregation reproduce the exact results. It is shown that the algorithm can obtain the large deviation functions for other kernels, including gelling ones, as well as the instanton trajectories for atypical times. The dependence of the autocorrelation times, both temporal and configurational, on the different parameters of the algorithm is also characterized.
