We propose, and illustrate via a neural network example, two different approaches to coarse-graining large heterogeneous networks. Both approaches are inspired from, and use tools developed in, methods for uncertainty quantification in systems with multiple uncertain parameters - in our case, the parameters are heterogeneously distributed on the network nodes. The approach shows promise in accelerating large scale network simulations as well as coarse-grained fixed point, periodic solution and stability analysis. We also demonstrate that the approach can successfully deal with structural as well as intrinsic heterogeneities.
@article{arxiv.1603.06643,
title = {Dimension reduction in heterogeneous neural networks: generalized Polynomial Chaos (gPC) and ANalysis-Of-VAriance (ANOVA)},
author = {Minseok Choi and Tom Bertalan and Carlo R. Laing and Ioannis G. Kevrekidis},
journal= {arXiv preprint arXiv:1603.06643},
year = {2016}
}