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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.
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