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We propose, and illustrate via a neural network example, two differentapproaches to coarse-graining large heterogeneous networks. Both approaches areinspired from, and use tools developed in, methods for uncertaintyquantification in systems with multiple uncertain parameters - in our case, theparameters are heterogeneously distributed on the network nodes. The approachshows promise in accelerating large scale network simulations as well ascoarse-grained fixed point, periodic solution and stability analysis. We alsodemonstrate that the approach can successfully deal with structural as well asintrinsic heterogeneities.

Dimension reduction in heterogeneous neural networks: generalized Polynomial Chaos (gPC) and ANalysis-Of-VAriance (ANOVA)