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.
Bibliographical noteFunding Information:
We thank I. Kanter, C. Kirst, B. Lünsmann, and M. Peer for valuable discussions and L. J. Deutsch for help with figure preparation. M.N. is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship. This study was supported by the Federal Ministry of Education and Research (BMBF; grant 03SF0472E) and the Max Planck Society (to M.T.). Author contributions: All authors conceived the research and contributed materials and analysis tools. M.N. and M.T. designed the research. All authors worked out the theory. M.N. and J.C. developed the algorithms and carried out the numerical experiments. All authors analyzed the data, interpreted the results, and wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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