论文标题
部分可观测时空混沌系统的无模型预测
Chain recurrence rates and topological entropy for free semigroup actions
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Misiurewicz[19]introducedtheconceptofpseudo-entropyandproved this quantity coincides with topological entropy. Richeson et al. [21] obtained the lower bounded of topological entropy by means of the definition of pseudo-entropy. This paper aims to generalize the main results obtained by Misiurewicz and Rich-eson et al. to free semigroup actions. Firstly, the pseudo-entropy is introduced for free semigroup actions, and it is shown that the pseudo-entropy coincides with the topological entropy defined by Bufetov [9]. Secondly, these concepts of the chain recurrence, the chain mixing, the chain recurrence time, and the chain mixing time for free semigroup actions are introduced, and the upper bounds of these recurrence times are given. Furthermore, a lower bound of topological entropy is given by the lower box dimension and the chain mixing time using the definition of pseudo-entropy for free semigroup actions. Thirdly, the structure of chain transitive systems for free semigroup actions is discussed.
