Data-driven coarse-graining and multiscale model reduction for ODEs and PDEs  

Project description

Project in collaboration with prof. Tom Hudson (University of Warwick), prof. Lorenzo Rovigatti (Roma La Sapienza), Dr. Nicodemo Di Pasquale (University of Manchester)

Many theoretical tools have been recently developed to reduce the complexity of high-dimensional non-linear ODEs or highly-resolved multiscale PDEs. These have now an enormous importance in computational chemistry, continuum mechanics, fluid dynamics, and dynamical systems in general. One of these bottom-up formal approaches is the Mori-Zwanzig projection formalism for dynamical systems. At the same time, also data-driven top-down methods, have been widely studied in machine learning and in numerical analysis. In this project, we aim to connect these theoretical and numerical tools to make them applicable for practical applications, such as the molecular dynamics simulation of complex molecule chains, or the relaxation to equilibrium of non-linear reaction-diffusion equations. In the first case, we can rely on the Hamiltonian structure of the full-resolution model, while the latter can be analysed through model decomposition or spectral analysis. The objective is to develop and implement flexible numerical approaches to deal with the model reduction of different model problems, by combining analytical derivations with numerical simulation data.