  Several studies have proposed constraints under which a low dimensional
representation can be derived from large-scale real-world networks exhibiting
complex nonlinear dynamics. Typically, these representations are formulated
under certain assumptions, such as when solutions converge to attractor states
using linear stability analysis or using projections of large-scale dynamical
data into a set of lower dimensional modes that are selected heuristically.
Here, we propose a generative framework for selection of lower dimensional
modes onto which the entire network dynamics can be projected based on the
symmetry of the input distribution for a large-scale network driven by external
inputs, thus relaxing the heuristic selection of modes made in the earlier
reduction approaches. The proposed mode reduction technique is tractable
analytically and applied to different kinds of real-world large-scale network
scenarios with nodes comprising of a) Van der Pol oscillators b) Hindmarsh-Rose
neurons. These two demonstrations elucidate how order parameter is conserved at
original and reduced descriptions thus validating our proposition.
