Accelerated simulation of a neuronal population via mathematical model order reduction

Abstract

Mathematical modeling of biological neuronal networks is important in order to increase understanding of the brain and develop systems capable of brain-like learning. While mathematical analysis of these comprehensive, stochastic, and complex models is intractable, and their numerical simulation is very resource intensive, mean-field modeling is an effective tool in enabling the analysis of these models. The mean-field approach allows the study of populations of biophysically detailed neurons with some assumptions of the mean behaviour of the population, but ultimately requires numerical solving of highdimensional differential equation systems. Mathematical model order reduction methods can be employed to accelerate the analysis of high-dimensional nonlinear models with a purely softwarebased approach. Here we compare state-of-the-art methods for improving the simulation time of a neuronal mean-field model and show that a nonlinear Fokker-Planck-McKean-Vlasov model can be accurately approximated in low-dimensional subspaces with these methods. Using Proper Orthogonal Decomposition and different variations of the Discrete Empirical Interpolation Method, we improved the simulation time by over three orders of magnitude while achieving low approximation error.