Research: Coarse-graining

Many phenomena are modelled by high-dimensional systems of nonlinear differential equations. While such models are accurate in principle, they present a series of challenges: 

• They often depend on a very large collection of parameters which are hard to fit to real-world data; and

• Their high dimensionality makes them difficult to simulate accurately and to interpret through identification of key features.

With the advent of mass data collection and storage, addressing these challenges has become ever more crucial to enable us to harness these new technologies.

One thread of my own research is focused on deploying the Mori-Zwanzig formalism to try to develop new statistical models of dynamical processes arising in Materials Science in particular, but new theoretical tools have a wide range of applications.

A more recent development is a collaboration with Civil Engineers applying averaging and upscaling techniques to connect mathematical and numerical models of porous media at different scales.