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Accelerated simulation of a neuronal population via mathematical model order reduction

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Details

Original languageEnglish
Title of host publicationProceedings of the IEEE International Conference on Artificial Intelligence Circuits and Systems
PublisherIEEE Xplore
Publication statusAccepted/In press - 10 Dec 2019
Publication typeA4 Article in a conference publication
EventIEEE International Conference on Artificial Intelligence Circuits and Systems -
Duration: 9 Jan 2020 → …

Conference

ConferenceIEEE International Conference on Artificial Intelligence Circuits and Systems
Period9/01/20 → …

Abstract

Mathematical modeling of biological neuronal net-
works 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 high-
dimensional differential equation systems. Mathematical model
order reduction methods can be employed to accelerate the anal-
ysis of high-dimensional nonlinear models with a purely software-
based 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.