We devise a machine learning technique to solve the general problem of inferring network links that have time delays using only time series data of the network nodal states. This task has applications in many fields, e.g., from applied physics, data science, and engineering to neuroscience and biology. Our approach is to first train a type of machine learning system known as reservoir computing to mimic the dynamics of the unknown network. We then use the trained parameters of the reservoir system output layer to deduce an estimate of the unknown network structure. Our technique, by its nature, is noninvasive but is motivated by the widely used invasive network inference method, whereby the responses to active perturbations applied to the network are observed and employed to infer network links (e.g., knocking down genes to infer gene regulatory networks). We test this technique on experimental and simulated data from delay-coupled optoelectronic oscillator networks, with both identical and heterogeneous delays along the links. We show that the technique often yields very good results, particularly if the system does not exhibit synchrony. We also find that the presence of dynamical noise can strikingly enhance the accuracy and ability of our technique, especially in networks that exhibit synchrony.

中文翻译：

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噪声延迟耦合网络的机器学习链路推理与光电实验测试

我们设计了一种机器学习技术来解决仅使用网络节点状态的时间序列数据来推断具有时间延迟的网络链接的一般问题。这项任务在许多领域都有应用，例如，从应用物理学、数据科学和工程学到神经科学和生物学。我们的方法是首先训练一种称为储层计算的机器学习系统来模拟未知网络的动态。然后我们使用油藏系统输出层的训练参数来推断未知网络结构的估计。我们的技术就其性质而言是非侵入性的，但受到广泛使用的侵入性网络推理方法的推动，由此观察到对应用于网络的主动扰动的响应并用于推断网络链接（例如，敲除基因以推断基因调控网络）。我们在来自延迟耦合光电振荡器网络的实验和模拟数据上测试该技术，沿链路具有相同和异构延迟。我们表明该技术通常会产生非常好的结果，特别是如果系统不显示同步。我们还发现动态噪声的存在可以显着提高我们技术的准确性和能力，尤其是在表现出同步性的网络中。