Coarse-graining for coupled oscillators: a case study in discovering low-dimensional dynamics


Numerical simulations form a backbone of modern science. We investigate the following question: given a simulation of some dynamical process, does there exist a good lower-dimensional representation? If so, finding such a representation may offer both computational speedup and fundamental insight into the dynamics of interest. To approach this question in the abstract, we infer coarse-grained equations of motion that describe a heterogeneous population of oscillators with a modular coupling structure. We choose this system because it is known to exhibit a transition from high- to low-dimensional behavior, and that low-dimensional behavior is well-described by equations of a known form. We conclude by exploring ways to move forward by systematically discarding several of the simplifying assumptions at play.

Slides here

I also gave (versions of) this talk at

  • CNLS in September 2018
  • APS Far West section meeting at Cal State Fullerton in October 2018
  • UC Davis student-run math/applied math seminar in November 2018
  • SIAM Conference on Applications of Dynamical Systems (DS19) in Snowbird, UT, May 2019