EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation

Lead Research Organisation: University of Oxford
Department Name: Mathematical Institute


Probabilistic modelling permeates all branches of engineering and science, either in a fundamental way, addressing randomness and uncertainty in physical and economic phenomena, or as a device for the design of stochastic algorithms for data analysis, systems design and optimisation. Probability also provides the theoretical framework which underpins the analysis and design of algorithms in Data Science and Artificial Intelligence.

The "CDT in Mathematics of Random Systems" is a new partnership in excellence between the Oxford Mathematical Institute, the Oxford Dept of Statistics, the Dept of Mathematics at Imperial College and multiple industry partners from the healthcare, technology and financial services sectors, whose goal is to establish an internationally leading PhD training centre for probability and its applications in physics, finance, biology and Data Science, providing a national beacon for research and training in stochastic modelling and its applications, reinforcing the UK's position as an international leader in this area and meeting the needs of industry for experts with strong analytical, computing and modelling skills.

We bring together two of the worlds' best and foremost research groups in the area of probabilistic modelling, stochastic analysis and their applications -Imperial College and Oxford- to deliver a consolidated training programme in probability, stochastic analysis, stochastic simulation and computational methods and their applications in physics, biology, finance, healthcare and Data Science. Doctoral research of students will focus on the mathematical modelling of complex physical, economic and biological systems where randomness plays a key role, covering mathematical foundations as well as specific applications in collaboration with industry partners. Joint projects with industrial partners across several sectors -technology, finance, healthcare- will be used to sharpen research questions, leverage EPSRC funding and transfer research results to industry.

Our vision is to educate the next generation of PhDs with unparalleled, cross-disciplinary expertise, strong analytical and computing skills as well as in-depth understanding of applications, to meet the increasing demand for such experts within the Technology sector, the Financial Service sector, the Healthcare sector, Government and other Service sectors, in partnership with industry partners from these sectors who have committed to co-funding this initiative.


This proposal reaches across various areas of pure and applied mathematics and Data Science and addresses the EPSRC Priority areas of (15. Mathematical and Computational Modelling), (22. Pure Mathematics and its Interfaces) ; however, the domain it covers is cross-disciplinary and broader than any of these priority areas taken in isolation. Probabilistic methods and algorithms form the theoretical foundation for the burgeoning area of Data Science and AI, another EPSRC Priority area which we plan to address, in particular through industry partnerships with AI/technology/data science firms.


By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to
- sharpening the UK's research lead in this area and training a new generation of mathematical scientists who can tackle scientific challenges in the modelling of complex, simulation and control of complex random systems in science and industry, and explore the exciting new avenues in mathematical research many of which have been pioneered by researchers in our two partner institutions;
- train the next generation of experts able to deploy sophisticated data driven models and algorithms in the technology, finance and healthcare sectors

Planned Impact

Probabilistic modelling permeates the Financial services, healthcare, technology and other Service industries crucial to the UK's continuing social and economic prosperity, which are major users of stochastic algorithms for data analysis, simulation, systems design and optimisation. There is a major and growing skills shortage of experts in this area, and the success of the UK in addressing this shortage in cross-disciplinary research and industry expertise in computing, analytics and finance will directly impact the international competitiveness of UK companies and the quality of services delivered by government institutions.
By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to
- sharpening the UK's research lead in this area and
- meeting the needs of industry across the technology, finance, government and healthcare sectors


The explosion of novel research areas in stochastic analysis requires the training of young researchers capable of facing the new scientific challenges and maintaining the UK's lead in this area. The partners are at the forefront of many recent developments and ideally positioned to successfully train the next generation of UK scientists for tackling these exciting challenges.
The theory of regularity structures, pioneered by Hairer (Imperial), has generated a ground-breaking approach to singular stochastic partial differential equations (SPDEs) and opened the way to solve longstanding problems in physics of random interface growth and quantum field theory, spearheaded by Hairer's group at Imperial. The theory of rough paths, initiated by TJ Lyons (Oxford), is undergoing a renewal spurred by applications in Data Science and systems control, led by the Oxford group in conjunction with Cass (Imperial). Pathwise methods and infinite dimensional methods in stochastic analysis with applications to robust modelling in finance and control have been developed by both groups.
Applications of probabilistic modelling in population genetics, mathematical ecology and precision healthcare, are active areas in which our groups have recognized expertise.


The large-scale computerisation of financial markets and retail finance and the advent of massive financial data sets are radically changing the landscape of financial services, requiring new profiles of experts with strong analytical and computing skills as well as familiarity with Big Data analysis and data-driven modelling, not matched by current MSc and PhD programs. Financial regulators (Bank of England, FCA, ECB) are investing in analytics and modelling to face this challenge. We will develop a novel training and research agenda adapted to these needs by leveraging the considerable expertise of our teams in quantitative modelling in finance and our extensive experience in partnerships with the financial institutions and regulators.


Probabilistic algorithms, such as Stochastic gradient descent and Monte Carlo Tree Search, underlie the impressive achievements of Deep Learning methods. Stochastic control provides the theoretical framework for understanding and designing Reinforcement Learning algorithms. Deeper understanding of these algorithms can pave the way to designing improved algorithms with higher predictability and 'explainable' results, crucial for applications.
We will train experts who can blend a deeper understanding of algorithms with knowledge of the application at hand to go beyond pure data analysis and develop data-driven models and decision aid tools
There is a high demand for such expertise in technology, healthcare and finance sectors and great enthusiasm from our industry partners. Knowledge transfer will be enhanced through internships, co-funded studentships and paths to entrepreneurs


10 25 50