Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
For computational neuroscience, this provides a method to analyze neural network dynamics at multiple scales without deriving closed-form equations, but the approach is incremental as it applies existing techniques to a specific network topology.
The paper applies the Equation-Free approach to study neural dynamics on random regular graphs, computing coarse-grained equilibrium bifurcation diagrams and stability without explicit macroscopic closures, and performs rare-events analysis via an effective Fokker-Planck equation.
We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables.