Mathematics Colloquium: Mesoscopic dynamics of large ODE systems
4:10 pm; Neill Hall 5W
Abstract: The main question addressed in the talk is as follows. How to produce computationally feasible and practically useful simulations of large ODE systems? A typical size of such systems is 107 unknowns or more. In a typical application, actual solutions are rarely needed. Instead, one might be interested in simulating evolution of certain functionals of solutions, called observables. The number of such functionals can be small (1- 10). We present some new ideas on how to obtain a closed system governing evolution of observables, starting from an ODE system. The proposed approach is based on space-time averaging and concentration inequalities from probability theory.