points $y_i(t), \dots y_i(t-k)$, for a given number $k$ provided by the approach. Here, we focus on the case when $k=1$, which occurs in many real-world examples, and discuss cases with $k\ge2$ in the Supplementary Materials. This means that $$\begin{aligned}
y_i(t+1) = g_i(y(t))+ \xi_i(t) \label{eq:meanfield}\end{aligned}$$ where $$g_i=f_i(y_i(t))+\beta_i v(y_i(t))$$ is a low-dimensional law that approximates the evolution of $y_i(t)$. We first employ Takens reconstruction to estimate $g_i$ and coarsely classify the nodes by their degrees. For instance, in rich-club motifs, the network has low-degree nodes organised in communities and high-degree in the rich-club. Since $\beta_i=\alpha k_i$ is small for low-degree nodes $i$, the evolution rules at such nodes will be similar to the isolated dynamics. Thus we identify which nodes are low-degree nodes and we can recover the local dynamics $f$. Next, we use Eq. (\[eq:meanfield\]) and a classification of nodes by their time-series, to obtain the coupling function and estimate the degree distribution $k_i$ and the coupling parameter $\alpha$. More precisely, an effective network is obtained in three main steps (see Methods for additional details):

-   [**Reduced dynamics.**]{} Since the fluctuation term $\xi_i(t)$ is small, the rule $g_i$ can be estimated fitting the points $(y_i(t), y_i(t+1))$ using machine-learning techniques. Here, 