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Networks of coupled oscillators are some of the most studied objects in thetheory of dynamical systems. Two important areas of current interest are thestudy of synchrony in highly disordered systems and the modeling of systemswith adaptive network structures. Here, we present a single approach to both ofthese problems in the form of "KuraNet", a deep-learning-based system ofcoupled oscillators that can learn to synchronize across a distribution ofdisordered network conditions. The key feature of the model is the replacementof the traditionally static couplings with a coupling function which can learnoptimal interactions within heterogeneous oscillator populations. We apply ourapproach to the eponymous Kuramoto model and demonstrate how KuraNet can learndata-dependent coupling structures that promote either global or clustersynchrony. For example, we show how KuraNet can be used to empirically explorethe conditions of global synchrony in analytically impenetrable models withdisordered natural frequencies, external field strengths, and interactiondelays. In a sequence of cluster synchrony experiments, we further show howKuraNet can function as a data classifier by synchronizing into coherentassemblies. In all cases, we show how KuraNet can generalize to both new dataand new network scales, making it easy to work with small systems and formhypotheses about the thermodynamic limit. Our proposed learning-based approachis broadly applicable to arbitrary dynamical systems with wide-rangingrelevance to modeling in physics and systems biology.

KuraNet: Systems of Coupled Oscillators that Learn to Synchronize