论文标题
部分可观测时空混沌系统的无模型预测
An upper bound of the numbers of minimally intersecting filling coherent pairs
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。
Let $S_g$ denoting the genus $g$ closed orientable surface. An {\em origami} (or flat structure) on $S_g$ is obtained from a finite collection of unit Euclidean squares by gluing each right edge to a left one and each top edge to a bottom one. Coherent filling pairs of simple closed curves, $(α,β)$ in $S_g$ are pairs for which their minimal intersection is equal to their algebraic intersection. And, a minimally intersecting filling of $(α,β)$ in $S_g$ is a pair whose intersection number is the minimal among all filling pairs of $S_g$. A coherent pair of curves is naturally associated with an origami on $S_g$, and a minimally intersecting filling coherent pair of curves has the smallest number of squares in all origamis on $S_g$. Our main result introduce an algorithm to count the numbers of minimal filling pairs on $S_g$, and establish a new upper bound of this count using Ménage Problem.
