PhD Scholarship project: Data-driven modelling and prediction of complex systems

About the project

About the Project The overarching objective is to utlise existing state-of-the art data-driven methodologies, and, building on recent efforts in the group, to develop new ones as needed, to efficiently simulate and accurately predict complex systems. Of particular interest are families of continuous deep architectures, which have recently re-emerged as "neural ordinary-differential equations (NODEs)" and physics-informed neural networks (PINNs). Specifically, NODEs will be utilised in the first instance to analyse the dynamics of a set of ODEs [which for sufficiently large number of ODEs yield a partial-differential equation (PDE)], followed by stochastic-differential equations (SDEs) and ultimately SPDEs. This work will be complemented by the use of PINNs where NNs will be trained to act as the numerical solution of ODEs/PDEs/SDEs/SPDEs. A number of prototypical systems will be considered in order of increased complexity. These include the Lorenz system, a set of three ODEs obtained from the Rayleigh-Benard convection between two parallel plates (which in turn can be viewed as a model of the atmosphere) via dimension reduction. The Lorenz system exhibts non-trivial behaviour including transition to chaos. Particular emphasis will be given to a systematic sensitivity analysis to assess the predictability of NODEs for the prototypical systems we will consider. This scholarship is open to all applicants regardless of their fee status. It covers both tuition fees and a tax-free contribution to maintenance costs of £25,000 per annum for 42 months. The Department of Chemical Engineering at Imperial College London offers an advanced 3-4-year research degree that provides in-depth specialist training and knowledge in a topical area pertaining to Chemical Engineering and related Engineering and Science disciplines. The Department has state-of-the-art experimental and computational facilities and is the home of the Automated high-throughput platform suite , the Sargent Centre for Process Systems Engineering and the Sustainable Futures Lab . The Department holds a Silver Athena Swan award for good practice in supporting academic women and gender equality renewed in 2024. This award recognises the good practices already in place for supporting women at all stages as well as our commitment to removing barriers to equal progress and achievement. Deadline: 01 November 2027 for the first selection round 11 January 2027 for the second selection round 01 March 2027 for the third selection round (subject to availability of scholarships) In order to be considered for the Chemical Engineering PhD Scholarships, you will need to submit your PhD application for admission through the online admissions system . Full details on the application and selection process can be found on our webpages . We encourage all interested applicants to contact Prof Kalliadasis ( s.kalliadasis@imperial.ac.uk ) before making an application.

Research areas