Model-reduction, or coarse-graining, refers to the process of taking a model governing many degrees of freedom and approximating it by a model with a lower number of degrees of freedom. For complex models such as those used in molecular dynamics, the process of coarse-graining enables longer and larger simulations with given computational resources, and so is frequently used by practitioners. Motivated by this application, I will discuss the coarse-graining of stochastic dynamical systems and discuss the Mori-Zwanzig formalism, which provides a framework within which one may evaluate the accuracy of a coarse-grained model. I will then present recent rigorous mathematical results on the accuracy of coarse-grained systems in this context obtained with Helen Li.
Pizza lunch will be served before the talk, beginning at 12:00.