Speeding up simulation of large-scale dynamical networks by aggregation

Abstract:

Dynamical models of systems across many branches of science and engineering can be described in terms of massively many entities interacting over large-scale networks. Examples are models of opinion formation, rumour spreading, traffic networks, collaboration networks, social networks, protein-interaction networks, epidemiology.

 

These models can often be mathematically represented as stochastic processes or differential equations. Unfortunately, in all but special cases, these models do not enjoy analytical solutions, imposing analysis based on stochastic simulators and numerical solvers. As a consequence, the computational cost increases with the model size, hindering our capability of dealing with complex large-scale models of real-world systems.

 

Using real-world examples, this talk will present an array of recent techniques that tame the complexity of complex large-scale models by aggregating their constituting systems of equations, leading to lower-dimensional systems that preserve the original dynamics in some appropriate, formal sense.