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Methods for reconstructing the topology of complex networks fromtime-resolved observations of node dynamics are gaining relevance acrossscientific disciplines. Of biggest practical interest are methods that make noassumptions about properties of the dynamics, and can cope with noisy, shortand incomplete trajectories. Ideal reconstruction in such scenario requires andexhaustive approach of simulating the dynamics for all possible networkconfigurations and matching the simulated against the actual trajectories,which of course is computationally too costly for any realistic application.Relying on insights from equation discovery and machine learning, we hereintroduce \textit{decoupling approximation} of dynamical networks and propose anew reconstruction method based on it. Decoupling approximation consists ofmatching the simulated against the actual trajectories for each nodeindividually rather than for the entire network at once. Despite drasticreduction of the computational cost that this approximation entails, we findour method's performance to be very close to that of the ideal method. Inparticular, we not only make no assumptions about properties of thetrajectories, but provide strong evidence that our methods' performance islargely independent of the dynamical regime at hand. Of crucial relevance forpractical applications, we also find our method to be extremely robust to bothlength and resolution of the trajectories and relatively insensitive to noise.

Decoupling approximation robustly reconstructs directed dynamical networks