Coarse-Graining for Coupled Oscillators: A case study in discovering low-dimensional dynamics

Quantitative science has produced successful models of the 
world at scales spanning dozens of orders of magnitude in space, time, 
and energy. While in principle, the most finely detailed models are 
sufficient to reproduce the predictions of any less-detailed model, 
there is clearly scientific value in deriving and studying models that 
do not resolve details that are not directly relevant to the question at 
hand. The procedure of systematically reducing the degrees of freedom of 
a model goes by many names depending on context (renormalization group 
in statistical physics) but can be generally be referred to as "model 
reduction". In this talk I will discuss progress towards general 
principles of model reduction obtained by studying synchronization of 
phase oscillators on a modular network. This system is an ideal test-bed 
because it exhibits a controllable transition from high- to 
low-dimensional behavior; moreover, the resulting low-dimensional 
behavior is well-described by coarse-grained equations of a known form.