  In this paper we explore how concepts of high-dimensional data compression
via random projections onto lower-dimensional spaces can be applied for
tractable simulation of certain dynamical systems modeling complex
interactions. In such systems, one has to deal with a large number of agents
(typically millions) in spaces of parameters describing each agent of high
dimension (thousands or more). Even with today's powerful computers, numerical
simulations of such systems are prohibitively expensive. We propose an approach
for the simulation of dynamical systems governed by functions of adjacency
matrices in high dimension, by random projections via Johnson-Lindenstrauss
embeddings, and recovery by compressed sensing techniques. We show how these
concepts can be generalized to work for associated kinetic equations, by
addressing the phenomenon of the delayed curse of dimension, known in
information-based complexity for optimal numerical integration problems in high
dimensions.
