Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about properties of the dynamics, and can cope with noisy, short and incomplete trajectories. Ideal reconstruction in such scenario requires and exhaustive approach of simulating the dynamics for all possible network configurations 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 here introduce \textit{decoupling approximation} of dynamical networks and propose a new reconstruction method based on it. Decoupling approximation consists of matching the simulated against the actual trajectories for each node individually rather than for the entire network at once. Despite drastic reduction of the computational cost that this approximation entails, we find our method's performance to be very close to that of the ideal method. In particular, we not only make no assumptions about properties of the trajectories, but provide strong evidence that our methods' performance is largely independent of the dynamical regime at hand. Of crucial relevance for practical applications, we also find our method to be extremely robust to both length and resolution of the trajectories and relatively insensitive to noise.