Abstract
We devise a machine learning technique to solve the general problem of inferring network links that have time-delays. The goal is to do this purely from time-series data of the network nodal states. This task has applications in fields ranging from applied physics and engineering to neuroscience and biology. To achieve this, we first train a type of machine learning system known as reservoir computing to mimic the dynamics of the unknown network. We formulate and test a technique that uses the trained parameters of the reservoir system output layer to deduce an estimate of the unknown network structure. Our technique, by its nature, is non-invasive, 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 opto-electronic oscillator networks. 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.
Highlights
Evolving complex networks are ubiquitous in natural and technological systems [1]
(i) Testing on experimental and simulated time-series datasets from networks, we find that, in the absence of dynamical noise, our method yields extremely good results, as long as there is no synchrony in the system
(ii) We find that dynamical noise and/or a moderate amount of link time delay heterogeneity can greatly enhance the performance of our method when synchrony is present, provided that the noise amplitude or link time delay heterogeneity is large enough to perturb the synchrony
Summary
Evolving complex networks are ubiquitous in natural and technological systems [1]. Determination of the connectivity in nervous systems [9,10,11], mapping of interactions between genes [12] and proteins in biochemical networks [13], distinguishing relationships between species in ecological networks [14,15], understanding the causal dependencies between elements of the global climate [16], and charting of the invisible dark web of the Internet [17] In many of these problems, we can only passively observe time series data for the states of the network nodes and cannot actively perturb the systems in any way. Our results provide a clear demonstration that reservoir computing, and possibly other related machine learning methods, can provide accurate network inference for real networks, including situations where complications like noise and time delays in the coupling are present. V with further discussion, suggested future directions, and possible generalizations of our method
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