论文标题
部分可观测时空混沌系统的无模型预测
Complete cavity map of the C. elegans connectome
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。
Network structure or topology is the basis for understanding complex systems. Recently, higher-order structures have been considered as a new research direction that can provide new perspectives and phenomena. However, most existing studies have focused on simple 1-cycles and triangles, and few have explored the higher-order and non-trivial cycles. The current study focused on the cavity, which is a non-trivial cycle. We proposed a method to compute cavities with different orders based on pruning in the boundary matrix and calculated all cavities of the neural network of Caenorhabditis elegans (\emph{C. elegans}) neural network. This study reports for the first time a complete cavity map of C. elegans neural network, developing a new method for mining higher-order structures that can be applied by researchers in neuroscience, network science and other interdisciplinary fields to explore higher-order structural markers of complex systems.
