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Several studies have proposed constraints under which a low dimensionalrepresentation can be derived from large-scale real-world networks exhibitingcomplex nonlinear dynamics. Typically, these representations are formulatedunder certain assumptions, such as when solutions converge to attractor statesusing linear stability analysis or using projections of large-scale dynamicaldata into a set of lower dimensional modes that are selected heuristically.Here, we propose a generative framework for selection of lower dimensionalmodes onto which the entire network dynamics can be projected based on thesymmetry of the input distribution for a large-scale network driven by externalinputs, thus relaxing the heuristic selection of modes made in the earlierreduction approaches. The proposed mode reduction technique is tractableanalytically and applied to different kinds of real-world large-scale networkscenarios with nodes comprising of a) Van der Pol oscillators b) Hindmarsh-Roseneurons. These two demonstrations elucidate how order parameter is conserved atoriginal and reduced descriptions thus validating our proposition.

Generative framework for dimensionality reduction of large scale network of non-linear dynamical systems driven by external input