  Higher-order interactions play a key role for the stability and function of a
complex system. However, how to identify them is still an open problem. Here,
we propose a method to fully reconstruct the structural connectivity of a
system of coupled dynamical units, identifying both pairwise and higher-order
interactions from the system time evolution. Our method works for any dynamics,
and allows the reconstruction of both hypergraphs and simplicial complexes,
either undirected or directed, unweighted or weighted. With two concrete
applications, we show how the method can help understanding the ecosystemic
complexity of bacterial systems, or the microscopic mechanisms of interaction
underlying coupled chaotic oscillators.
