Data-driven and kernel-based analysis of complex dynamical systems

The main focus of this project is the data-driven analysis of complex dynamical systems exhibiting multiple time scales.

Start date
Minimum of 3 years
Application deadline
Funding information

Full UK tuition fees and a tax-free stipend. This project is on offer in competition with a number of other projects for funding. This opportunity may be available with partial funding for overseas fees for exceptional applicants. However, funding for overseas students is limited and applicants are encouraged to find suitable funding themselves.

Funding source
University of Surrey
Supervised by


The main focus of this project is the data-driven analysis of complex dynamical systems exhibiting multiple time scales. Based only on simulation or measurement data, dominant dynamics or modes can be extracted, which are then, for instance, used for dimensionality reduction, the detection of metastable or coherent sets, system identification, or control. Due to the sheer size of the data sets, kernel-based approaches might be required to mitigate the curse of dimensionality. The successful candidate will develop, optimize, and implement novel methods to analyse high-dimensional time-series data in order to gain insight into the characteristic properties of the underlying system. Of particular interest are molecular dynamics problems (computation of stable conformations, analysis of protein folding processes), fluid flow problems (detection of coherent sets), and quantum mechanics problems (relationships with transfer operators, stochastic formulations of quantum mechanics, exploitation of symmetries/antisymmetries).

The successful candidate will receive comprehensive research training related to all aspects of the research and opportunities to participate in conferences, workshops and seminars to develop professional skills and research network.

We are able to offer this opportunity starting in October 2021, January 2022, April 2022 or July 2022.


Klus, S., Nüske, F., et al.: Data-Driven Model Reduction and Transfer Operator Approximation. J Nonlinear Sci 28, 985–1010 (2018). 

Eligibility criteria

Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.

Desired Qualifications

  • Experience in the simulation of complex dynamical systems (ODEs, SDEs, PDEs)
  • Interest in data-driven methods and machine learning as well as molecular dynamics, fluid dynamics, or quantum mechanics
  • Experience with kernel-based methods (reproducing kernel Hilbert spaces, kernel trick)
  • Programming skills in Matlab or Python

English Language requirements 

IELTS minimum 6.5 or above (or equivalent) with 6.0 in each individual category

How to apply

Applications should be submitted via the Mathematics PhD Research programme page on the "Apply" tab. Please clearly state the studentship title and supervisor on your application.

Contact details

Matthew Turner
26A AA 04
Telephone: +44 (0)1483 686183

Studentships at Surrey

We have a wide range of studentship opportunities available.