Coarse-graining the Dynamics of Complex Systems
In current modeling practice for complex systems, including agent-based and network-based simulations, the best available descriptions of a system often come at a fine level (atomistic, stochastic, individual-based) while the questions asked and the tasks required by the modeler (parametric analysis, optimization, control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches start by deriving macroscopic evolution equations from the microscopic models. I will review a mathematically inspired, systems-based computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly in an input-output mode. This “equation-free” approach circumvents the step of obtaining accurate macroscopic descriptions. I will discuss applications of this approach and its linking with recent developments in data mining algorithms, exploring large complex data sets to find good "reduction coordinates".
Yannis Kevrekidis, Princeton University, USA