MATHEMATICAL MODEL ORDER REDUCTION OF A FOKKER-PLANCK MEAN-FIELD MODEL
Research output: Other conference contribution › Paper, poster or abstract › Scientific
|Publication status||Published - 18 Sep 2019|
|Publication type||Not Eligible|
|Event||Bernstein Conference 2019 - Technische Universität Berlin, Berlin, Germany|
Duration: 18 Sep 2019 → 20 Dec 2019
|Conference||Bernstein Conference 2019|
|Period||18/09/19 → 20/12/19|
Using mean-field approximation, cells are grouped together into populations
based on their statistical similarities, in order to represent the dynamics of
the system in terms of the ensemble behaviour. These populations can then be
described by a probability density function expressing the distribution of
neuronal states at a given time. In this study we focus on a mean-field model of
a network of FitzHugh-Nagumo neurons with chemical synapses using the
Fokker-Planck formalism, which results in a nonlinear McKean-Vlasov partial
differential equation (PDE) . For numerical simulations the PDE is discretized in
space over three variables and a high-dimensional system, whose domain is a cube, is obtained.
The dimensionality, and hence simulation time, of discretized PDE systems can be reduced using mathematical model order reduction (MOR) methods. MOR methods are well established in engineering sciences, such as control theory. However, in computational neuroscience MOR is underutilised, although the potential benefits in enabling large-scale simulations are obvious .
Here we use recently developed advanced variants of the Discrete Empirical
Interpolation Method (DEIM)  to reduce a nonlinear mean-field model. The
system can be reduced with minimal information loss by deriving subspaces where the entire system is approximated with a small number of dimensions during the simulation phase, and after simulation the original model can be fully
reconstructed (see Fig. 1). By applying these methods, the simulation time of
the model is radically shortened, albeit not without dimension-dependent
approximation error. This can be particularly useful when attempting to model
whole-brain activity, for which there is an immediate demand in clinical and
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