https://doi.org/10.1140/epjst/e2016-02662-3
Regular Article
Dimension reduction in heterogeneous neural networks: Generalized Polynomial Chaos (gPC) and ANalysis-Of-VAriance (ANOVA)
1 Department of Chemical and Biological Engineering, Princeton University, Princeton, USA
2 Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand
3 Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, USA
a e-mail: minseokc@princeton.edu
b e-mail: bertalan@princeton.edu
c e-mail: c.r.laing@massey.ac.nz
d e-mail: yannis@princeton.edu
Received: 28 March 2016
Revised: 26 July 2016
Published online: 30 September 2016
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 (UQ) 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 computation and stability analysis. We also demonstrate that the approach can successfully deal with structural as well as intrinsic heterogeneities.
© EDP Sciences, Springer-Verlag, 2016
