Data-Driven Reconstruction of Firing Rate Dynamics in Brain Networks

This paper studies the reconstruction from data of firing rate dynamics in linear-threshold network models of brain activity. Instead of identifying the system paramaters directly, which would lead to a large number of variables and a highly non-convex objective function, the novelty of our approach stems from reformulating the identification problem as a scalar variable optimization of a discontinuous, nonconvex objective function. We formally show that the reformulated optimization problem has a unique solution and establish that it leads to the identification of all the desired system parameters. These results form the basis for the introduction of an algorithm to find the optimizer that identifies the different regions in the domain of definition of the objective function. The results not only validate the system identifiability but also provide the foundation for further research on data-driven control of firing rate dynamics. We demonstrate the algorithm effectiveness in simulation.