论文标题
通过储层计算预测非线性系统的维度标准
Dimensional criterion for forecasting nonlinear systems by reservoir computing
论文作者
论文摘要
在预测和复制混乱动力学系统中，储层计算机（RC）已被证明可作为替代模型。基于RCS的替代模型的质量至关重要取决于其最佳实现，涉及选择最佳储层拓扑和超参数。通过系统地应用贝叶斯高参数优化并使用各种拓扑的储层集合，我们表明，储层的连接仅在预测和复制足够复杂性的混乱系统中才有意义。 By applying RCs of different topology in forecasting and replicating the Lorenz system, a coupled Wilson-Cowan system, and the Kuramoto-Sivashinsky system, we show that simple reservoirs of unconnected nodes (RUN) outperform reservoirs of connected nodes for target systems whose estimated fractal dimension dimension is $d \lesssim 5.5$ and that linked对于$ d> 5.5 $的系统，储层更适合。这一发现对于评估储层计算方法和选择一种预测非线性系统测量的信号的方法非常重要。
Reservoir computers (RC) have proven useful as surrogate models in forecasting and replicating systems of chaotic dynamics. The quality of surrogate models based on RCs is crucially dependent on their optimal implementation that involves selecting optimal reservoir topology and hyperparameters. By systematically applying Bayesian hyperparameter optimization and using ensembles of reservoirs of various topology we show that connectednes of reservoirs is of significance only in forecasting and replication of chaotic system of sufficient complexity. By applying RCs of different topology in forecasting and replicating the Lorenz system, a coupled Wilson-Cowan system, and the Kuramoto-Sivashinsky system, we show that simple reservoirs of unconnected nodes (RUN) outperform reservoirs of connected nodes for target systems whose estimated fractal dimension dimension is $d \lesssim 5.5$ and that linked reservoirs are better for systems with $d > 5.5$. This finding is highly important for evaluation of reservoir computing methods and on selecting a method for prediction of signals measured on nonlinear systems.
