Effectively model dynamics, deterministic and stochastic, across multiple space and time scales

Abstract

A persistent feature of complex systems in engineering and science is the emergence of macroscopic, large scale, coherent behaviour from the interactions between microscopic agents (molecules, cells, grains) and also with their environment. In current modelling the underlying microscopic mechanisms are often known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. I overview a systematic dynamical approach to extract analytically compact, accurate, system level models of complex systems in physics and engineering. The methodology also supports transforming fine scale, microscopic, detailed descriptions of discrete dynamical systems across a multiscale hierarchy to a coarse system level discrete model. This approach illuminates the appearance of emergent dynamics in both deterministic and stochastic dynamics.