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nlin.CD混沌动力学1
2509.00848 2026-06-11 nlin.CD math.DS 版本更新

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

高维振荡器网络中低维读出的学习设计

Thomas Geert de Jong

AI总结 研究基于振荡器网络的储层计算,采用低维平均相位读出函数,通过连续极限和分岔分析,发现至少需要4个振荡器群体才能学习混沌目标动力学。

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AI中文摘要

本文研究了一种基于振荡器网络的储层计算机,该网络具有大量振荡器和低维读出。读出是关于每个振荡器群体平均相位的函数,因此提供了振荡器状态的鲁棒测量。我们考虑少量群体,从而得到低维读出。任务是时间序列预测。输入时间序列通过强迫项引入。经过训练阶段后,输入被学习。重要的是,训练权重被引入强迫项中,这意味着振荡器网络保持不变。因此,我们可以应用振荡器网络的经典方法。这里,我们通过使用Ott-Antonsen Ansatz考虑Kuramoto振荡器的连续极限。因此,出现了一个平均场储层计算机。然后通过耦合和强迫参数空间中的分岔来研究储层计算机的成功与失败。我们还将展示,当考虑相位状态上的读出时,平均相位读出可以自然出现。最后,我们给出数值证据,表明至少需要4个振荡器群体才能学习混沌目标动力学。

英文摘要

In this paper we investigate a oscillator network based reservoir computer with a large 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. Consequently, a mean field reservoir computer arises. 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.