  Revealing physical interactions in complex systems from observed collective
dynamics constitutes a fundamental inverse problem in science. Current
reconstruction methods require access to a system's model or dynamical data at
a level of detail often not available. We exploit changes in invariant
measures, in particular distributions of sampled states of the system in
response to driving signals, and use compressed sensing to reveal physical
interaction networks. Dynamical observations following driving suffice to infer
physical connectivity even if they are temporally disordered, are acquired at
large sampling intervals, and stem from different experiments. Testing various
nonlinear dynamic processes emerging on artificial and real network topologies
indicates high reconstruction quality for existence as well as type of
interactions. These results advance our ability to reveal physical interaction
networks in complex synthetic and natural systems.
