论文标题
部分可观测时空混沌系统的无模型预测
Common best proximity point theorems under proximal $F$-weak dominance in complete metric spaces
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。
Suppose that $S_1$ and $S_2$ are nonempty subsets of a complete metric space $(\mathcal{M},d)$ and $ϕ,ψ:S_1\to S_2$ are mappings. The aim of this work is to investigate some conditions on $ϕ$ and $ψ$ such that the two functions, one that assigns to each $x\in S_1$ exactly $d(x,ϕx)$ and the other that assigns to each $x\in S_1$ exactly $d(x,ψx)$, attain the global minimum value at the same point in $S_1$. We have introduced the notion of proximally $F$-weakly dominated pair of mappings and proved two theorems that guarantee the existence of such a point. Our work is an improvement of earlier work in this direction. We have also provided examples in which our results are applicable, but the earlier results are not applicable.
