论文标题
部分可观测时空混沌系统的无模型预测
A note on the distance spectra of co-centralizer graphs
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 $G$ be a finite non abelian group. The centralizer graph of $G$ is a simple undirected graph $Γ_{cent}(G)$, whose vertex set consists of proper centralizers of $G$ and two vertices are adjacent if and only if their cardinalities are identical [6]. We call the complement of the centralizer graph as the co-centralizer graph. In this paper, we investigate the distance, distance (signless) Laplacian spectra of co-centralizer graphs of some classes of finite non-abelian groups, and obtain some conditions on a group so that the co-centralizer graph is distance, distance (signless) Laplacian integral.
