Detecting Directional Coupling in Network Dynamical Systems via Kalman's Observability

Detecting coupling in network dynamical systems from time series is an open problem in the physics of complex systems. In this Letter, we tackle this issue from a control-theoretic perspective. Drawing inspiration from Kalman's notion of observability, we argue the presence of directional coupling between two units, X→Y, when X is detected as an internal state from the measurement of Y. We illustrate this approach on a series of analytically tractable systems, showcasing how it overcomes limitations of state-of-the-art methods for network inference.