论文标题
使用机器学习预测Hénon地图中的极端事件
Using Machine Learning to predict extreme events in the Hénon map
论文作者
论文摘要
机器学习（ML）启发的算法提供了一组灵活的工具，用于分析和预测混乱的动力学系统。我们在这里分析了一种算法在经典参数上在二维Hénon图中预测极端事件的性能。任务是确定轨迹在未来的设定时间步长之后是否会超过阈值。此任务在Hénon图的动力学中具有几何解释，我们用来评估本工作中使用的神经网络的性能。我们分析了ML模型对预测时间$ t $的成功率，培训样本$ N_T $的数量和网络$ N_P $的大小。我们观察到，为了保持一定准确性，$ n_t \ propto exp（2 h t）$和$ n_p \ propto exp（ht）$，其中$ h $是拓扑熵。在其他系统中也可以观察到动力学和ML参数的内在混乱性能之间的类似关系。
Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional Hénon map at the classical parameters. The task is to determine whether a trajectory will exceed a threshold after a set number of time steps into the future. This task has a geometric interpretation within the dynamics of the Hénon map, which we use to gauge the performance of the neural networks that are used in this work. We analyze the dependence of the success rate of the ML models on the prediction time $T$ , the number of training samples $N_T$ and the size of the network $N_p$. We observe that in order to maintain a certain accuracy, $N_T \propto exp(2 h T)$ and $N_p \propto exp(hT)$, where $h$ is the topological entropy. Similar relations between the intrinsic chaotic properties of the dynamics and ML parameters might be observable in other systems as well.
