Quantifying Coupled Dynamics in Phase-Space from State Distribution Snapshots (2507.18648v1)

Abstract: We quantify nonlinear interactions between coupled complex processes, when the system is subject to noise and not all its components are measurable. Our method is applicable even when the system cannot be continuously monitored over time, but is rather observed only in snapshots. Having only partial information about the local topology of the network and observations of relevant interacting variables is sufficient to translate qualitative knowledge of interactions into a quantitative characterization of the coupled dynamics. This approach turns a globally intractable problem into a sequence of solvable inference problems, to quantify complex interaction networks from incomplete snapshots of their statistical state.