Electrophysiological nature of neuronal networks allows to reveal various interactions between different cell units at a very short time-scales. One of the many challenges in analyzing these signals is to retrieve the morphology and functionality of a given network. In this work we developed a computational model, based on Reservoir Computing Network (RCN) architecture, which decodes the spatio-temporal data from electro-physiological measurements of neuronal cultures and reconstructs the network structure on a macroscopic domain, representing the connectivity between neuronal units. We demonstrate that the model can predict the connectivity map of the network with higher accuracy than the common methods such as Cross-Correlation and Transfer-Entropy. In addition, we experimentally demonstrate the ability of the model to predict a network response to a specific input, such as localized stimulus.