  Revealing the structure and dynamics of complex networked systems from
observed data is of fundamental importance to science, engineering, and
society. Is it possible to develop a universal, completely data driven
framework to decipher the network structure and different types of dynamical
processes on complex networks, regardless of their details? We develop a Markov
network based model, sparse dynamical Boltzmann machine (SDBM), as a universal
network structural estimator and dynamics approximator. The SDBM attains its
topology according to that of the original system and is capable of simulating
the original dynamical process. We develop a fully automated method based on
compressive sensing and machine learning to find the SDBM. We demonstrate, for
a large variety of representative dynamical processes on model and real world
complex networks, that the equivalent SDBM can recover the network structure of
the original system and predicts its dynamical behavior with high precision.

Physics and Society;Data Analysis, Statistics and Probability