unknown [*ergodic*]{} and [*chaotic*]{} map $\bm{F}$ (that is, $\| \bm{F} - \bm{F}_i \| \le \delta$, which is often the case in applications [@pinto2000; @eroglu2017]). $(b)$ The network connectivity is [*heterogeneous*]{}, which means that the number of incoming connections at a node $i$ (given by its degree $k_i = \sum_j A_{ij}$) varies widely across the network. More precisely, $k_i$ is larger for a few nodes called [*hubs*]{}. $(c)$ $\alpha$ is such that, denoting by $\Delta=\max_i k_i$ the maximum number of connections $\alpha \Delta$ is of the same magnitude of $\bm{DF}$. Assumptions $(a)$ and $(c)$ imply that the the total effect of the network on a node $i$, which is of the order $\alpha k_i$, ranges from small (for nodes $i$ with few incoming connections) to of order 1 for the hub nodes. A prime example is the cat cerebral cortex which possesses inter-connected regions split into communities with a hierarchical organization. This network has heterogeneous connectivity, chaotic motion and weak coupling [@scannell1993; @scannell1995; @zamora-lopez2010]. Other examples, includes the drosophila optic lobe network [@takemura2013; @garcia-perez2018]. For a given dataset, our effective network first tests whether the underlying system satisfies assumptions $(a)-(c)$, and, if so, reconstructs the model (see the Methods for more 