论文标题
部分可观测时空混沌系统的无模型预测
On groups with few subgroups not in the Chermak-Delgado lattice
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。
We investigate the question of how many subgroups of a finite group are not in its Chermak-Delgado lattice. The Chermak-Delgado lattice for a finite group is a self-dual lattice of subgroups with many intriguing properties. Fasolă and Tărnăuceanu asked how many subgroups are not in the Chermak-Delgado lattice and classified all groups with two or less subgroups not in the Chermak-Delgado lattice. We extend their work by classifying all groups with less than five subgroups not in the Chermak-Delgado lattice. In addition, we show that a group with less than five subgroups not in the Chermak--Delgado lattice is nilpotent. In this vein we also show that the only non-nilpotent group with five or fewer subgroups in the Chermak-Delgado lattice is S_3.
