标题： 高维振荡器网络中低维读出的学习设计 显示英文标题

标题： Designing learning in high dimensional oscillator networks with low dimensional read-out

摘要： 在本文中，我们研究如何配置一个具有大量振荡器和低维读出的振荡器网络储备计算机。 读出是相对于每个振荡器群体的平均相位的函数。 因此，这种读出提供了一种对振荡器状态的鲁棒测量。 我们考虑少量的群体，这导致了低维的读出。 在这里，任务是时间序列预测。 输入时间序列通过一个强迫项引入。 经过训练阶段后，输入被学习。 重要的是，训练权重被引入到强迫项中，这意味着振荡器网络本身未被改变。 因此，我们可以应用经典的方法来处理振荡器网络。 在这里，我们通过使用Ott-Antonsen假设来考虑Kuramoto振荡器的连续极限。 然后通过耦合和强迫参数空间中的分岔来研究储备计算机的成功与失败。 我们还将展示，当考虑相位状态的读出时，平均相位读出可以自然出现。 最后，我们提供了数值证据，表明至少需要4个振荡器群体才能学习混沌目标动力学。 显示英文摘要

摘要： In this paper we investigate how to configure an oscillator network based reservoir computer with a high number of oscillators and a low dimensional read-out. The read-out is a function on the average phases with respect to each oscillator population. Hence, this read-out provides a robust measurement of the oscillator states. We consider a low number of populations which leads to a low-dimensional read-out. Here, the task is time-series prediction. The input time-series is introduced via a forcing term. After a training phase the input is learned. Importantly, the training weights are introduced in the forcing term meaning that the oscillator network is left untouched. Hence, we can apply classical methods for oscillator networks. Here, we consider the continuum limit for Kuramoto oscillators by using the Ott-Antonsen Ansatz. The success and failure of the reservoir computer is then studied by bifurcations in the coupling and forcing parameter space. We will also show that the average phase read-out can naturally arise when considering the read-out on the phase states. Finally, we give numerical evidence that at least 4 oscillator populations are necessary to learn chaotic target dynamics.