Dimension reduction in physical and data sciences

The Mori-Zwanzig reduction methods with applications to transport problems

Xiantao Li

Penn State University


Mathematical models of complex physical processes often involve large number of degrees of freedom as well as events occurring on different time scales. Therefore, direct simulations based on these models face tremendous challenge. The focus of this talk is on the MZ (MZ) projection formalism, which has re-emerged recently as a powerful tool for reducing the dimension of a complex dynamical system. The goal is to mathematically derive a reduced model with much fewer variables, while still able to capture the essential properties of the system.