  This paper studies the data-driven reconstruction of firing rate dynamics of brain activity described by linear-threshold network models. Identifying the system parameters directly leads to a large number of variables and a highly non-convex objective function. Instead, our approach introduces a novel reformulation that incorporates biological organizational features and turns the identification problem into a scalar variable optimization of a discontinuous, non-convex objective function. We prove that the minimizer of the objective function is unique and establish that the solution of the optimization problem leads to the identification of all the desired system parameters. These results are the basis to introduce an algorithm to find the optimizer by searching the different regions corresponding to the domain of definition of the objective function. To deal with measurement noise in sampled data, we propose a modification of the original algorithm whose identification error is linearly bounded by the magnitude of the measurement noise. We demonstrate the effectiveness of the proposed algorithms through simulations on synthetic and experimental data. 
Efficient Reconstruction of Neural Mass Dynamics Modeled by   Linear-Threshold Networks