  The topology of interactions in network dynamical systems fundamentally
underlies their function. Accelerating technological progress creates massively
available data about collective nonlinear dynamics in physical, biological, and
technological systems. Detecting direct interaction patterns from those
dynamics still constitutes a major open problem. In particular, current
nonlinear dynamics approaches mostly require to know a priori a model of the
(often high dimensional) system dynamics. Here we develop a model-independent
framework for inferring direct interactions solely from recording the nonlinear
collective dynamics generated. Introducing an explicit dependency matrix in
combination with a block-orthogonal regression algorithm, the approach works
reliably across many dynamical regimes, including transient dynamics toward
steady states, periodic and non-periodic dynamics, and chaos. Together with its
capabilities to reveal network (two point) as well as hypernetwork (e.g., three
point) interactions, this framework may thus open up nonlinear dynamics options
of inferring direct interaction patterns across systems where no model is
known.
