Networks of coupled dynamical systems are successful models in diverse fields of science ranging from physics to neuroscience. The network interaction structure impacts the dynamics, in fact, many malfunctions are associated with disorders in the network structure. Yet, typically we cannot measure the interaction structure, we only have access to multivariate time series of nodes’ states. This led to much effort to reconstruct the network from multivariate data. This reconstruction problem is ill-posed for large networks leading to the reconstruction of false network structures. In this talk, I put forward an approach that uses the network dynamics’ statistical properties to ensure the exact reconstruction of weakly coupled sparse networks. Moreover, this approach exhibits robustness against noise. To demonstrate its efficacy, I illustrate its reconstruction power using experimental multivariate time series data obtained from optoelectronic networks.