  Reconstructing network dynamics from data is crucial for predicting the
changes in the dynamics of complex systems such as neuron networks; however,
previous research has shown that the reconstruction is possible under strong
constraints such as the need for lengthy data or small system size. Here, we
present a recovery scheme blending theoretical model reduction and sparse
recovery to identify the governing equations and the interactions of weakly
coupled chaotic maps on complex networks, easing unrealistic constraints for
real-world applications. Learning dynamics and connectivity lead to detecting
critical transitions for parameter changes. We apply our technique to realistic
neuronal systems with and without noise on a real mouse neocortex and
artificial networks.
