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

This project will be based at the University of Nottingham in the School of Mathematical Sciences in the group of Industrial and Applied Mathematics.

Many theoretical tools have been recently developed to reduce the complexity of high-dimensional non-linear ODEs or three-dimensional PDEs in complex environments. 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, for example, through their discrete (particle- or mesh-based) counterparts, or through classical spectral analysis. The objective of this project is to develop and implement flexible numerical approaches to deal with the model reduction, multi-scale approximation, and/or coarse-graining of a limited number of model problems, by combining analytical derivations with numerical simulation data. Real-world applications in complex fluids and porous media will be considered.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Applied Mathematics (or other field such as Physics or Engineering, showing evidence of deep knowledge of continuum transport models and numerical methods), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).