Towards reconstructions of variables of interest in nonlinear complex networks with an application in neuroscience

This article investigates the most effective way(s) to reconstruct target variables in networks of coupled ordinary differential equations. The differential equations describing the dynamics of nodes, as well as the considered coupling terms, are not constrained to be linear. The proposed reconstruction is built on a key theoretical elimination result. It consists in eliminating inner variables of the nodes that are not considered of interest. Building upon this result, we present an algorithm designed to systematically identify all possible step-by-step reconstruction of a target set of variables from a set of observed ones. In order to determine the best reconstruction pathways, we then define an index that takes into account the nature of expressions involved. To test our approach, we apply it to a biological neural network of Caenorhabditis elegans. This network is modeled using a phenomenological simple model with both linear and nonlinear coupling terms, illustrating the applicability of the method to complex and relevant biological systems.