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


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/S023925/1 31/03/2019 29/09/2027
2279494 Studentship EP/S023925/1 30/09/2019 31/03/2024 Alessandro Micheli
2281351 Studentship EP/S023925/1 30/09/2019 29/09/2023 Lancelot Da Costa
2272544 Studentship EP/S023925/1 30/09/2019 29/09/2023 Felix Prenzel
2272117 Studentship EP/S023925/1 30/09/2019 29/09/2023 Zheneng Xie
2281348 Studentship EP/S023925/1 30/09/2019 29/09/2023 Julian Sieber
2272186 Studentship EP/S023925/1 30/09/2019 29/09/2023 Julian Meier
2280105 Studentship EP/S023925/1 30/09/2019 29/09/2023 Harprit Singh
2280357 Studentship EP/S023925/1 30/09/2019 29/09/2023 Zan Zuric
2215977 Studentship EP/S023925/1 30/09/2019 29/09/2023 Benedikt Petko
2272535 Studentship EP/S023925/1 30/09/2019 16/05/2023 Alain Rossier
2269738 Studentship EP/S023925/1 30/09/2019 29/09/2023 Jonathan Tam
2272063 Studentship EP/S023925/1 30/09/2019 29/09/2024 Mateusz Mroczka
2279905 Studentship EP/S023925/1 30/09/2019 30/01/2024 Remy Messadene
2216902 Studentship EP/S023925/1 30/09/2019 30/11/2023 Victoria Klein
2444048 Studentship EP/S023925/1 30/09/2020 29/09/2024 Wei Xiong
2443932 Studentship EP/S023925/1 30/09/2020 29/09/2024 Ziheng Wang
2434258 Studentship EP/S023925/1 30/09/2020 29/09/2024 Benjamin Joseph
2440859 Studentship EP/S023925/1 30/09/2020 29/09/2024 Matthew Buckland
2441810 Studentship EP/S023925/1 30/09/2020 29/09/2024 Martin Geller
2441936 Studentship EP/S023925/1 30/09/2020 29/09/2024 Deborah Miori
2645916 Studentship EP/S023925/1 30/09/2020 29/09/2024 Matheus De Castro
2442356 Studentship EP/S023925/1 30/09/2020 29/09/2024 Dan Leonte
2435699 Studentship EP/S023925/1 30/09/2020 29/09/2024 Filippo De Angelis
2442363 Studentship EP/S023925/1 30/09/2020 29/09/2024 Yuriy Shulzhenko
2435698 Studentship EP/S023925/1 30/09/2020 29/09/2024 Philipp Jettkant
2440959 Studentship EP/S023925/1 30/09/2020 29/09/2024 Aldair Petronilia
2443859 Studentship EP/S023925/1 30/09/2020 29/09/2024 Aymeric ViƩ
2442024 Studentship EP/S023925/1 30/09/2020 12/05/2021 Milan Pache
2443943 Studentship EP/S023925/1 30/09/2020 29/09/2024 Fabrice Wunderlich
2442015 Studentship EP/S023925/1 30/09/2020 29/09/2024 Marcello Monga
2442362 Studentship EP/S023925/1 30/09/2020 29/09/2024 Luca Gerolla
2442028 Studentship EP/S023925/1 30/09/2020 29/09/2024 Thomas Tendron
2670173 Studentship EP/S023925/1 30/09/2020 29/09/2024 Martin Geller
2435718 Studentship EP/S023925/1 30/09/2020 29/09/2024 Michael Giegrich
2602125 Studentship EP/S023925/1 30/09/2021 29/09/2025 Giuseppe Tenaglia
2602130 Studentship EP/S023925/1 30/09/2021 29/09/2025 Roan Talbut
2602120 Studentship EP/S023925/1 30/09/2021 29/09/2025 Lorenzo Lucchese
2602127 Studentship EP/S023925/1 30/09/2021 29/09/2025 Martin Peev
2596025 Studentship EP/S023925/1 30/09/2021 29/09/2025 Milena Vuletic
2602122 Studentship EP/S023925/1 30/09/2021 29/09/2025 Owen Futter
2596017 Studentship EP/S023925/1 30/09/2021 29/09/2025 Shyam Popat
2594661 Studentship EP/S023925/1 30/09/2021 29/09/2025 Mark Jennings
2601859 Studentship EP/S023925/1 30/09/2021 29/09/2025 William Turner
2602126 Studentship EP/S023925/1 30/09/2021 29/09/2025 Bernat Bassols Cornudella
2602131 Studentship EP/S023925/1 30/09/2021 30/12/2025 Joseph Mulligan
2594682 Studentship EP/S023925/1 30/09/2021 29/09/2025 Yifan Jiang
2592790 Studentship EP/S023925/1 30/09/2021 29/09/2025 Vladislav Cherepanov
2594689 Studentship EP/S023925/1 30/09/2021 29/09/2025 Rivka Maclaine Mitchell
2602638 Studentship EP/S023925/1 30/09/2021 29/09/2025 Akshunna Dogra
2737145 Studentship EP/S023925/1 30/09/2022 29/09/2026 Julius Villar
2751196 Studentship EP/S023925/1 30/09/2022 29/09/2026 Timothy Kang
2733794 Studentship EP/S023925/1 30/09/2022 29/09/2026 Nicholas Daultry Ball
2752070 Studentship EP/S023925/1 30/09/2022 29/09/2026 Nicola Muca Cirone
2897811 Studentship EP/S023925/1 30/09/2022 29/09/2026 Dmitrii MINTS
2753653 Studentship EP/S023925/1 30/09/2022 29/09/2026 Timothy Kang
2751231 Studentship EP/S023925/1 30/09/2022 29/09/2026 Vincent Goverse
2733881 Studentship EP/S023925/1 30/09/2022 29/09/2026 Jad Hamdan
2733955 Studentship EP/S023925/1 30/09/2022 29/09/2026 Adam Jones
2734009 Studentship EP/S023925/1 30/09/2022 29/09/2026 Jacob Mercer
2734087 Studentship EP/S023925/1 30/09/2022 29/09/2026 Olivia Pricilia
2733979 Studentship EP/S023925/1 30/09/2022 29/09/2026 Chun Hei Lam
2734079 Studentship EP/S023925/1 30/09/2022 29/09/2026 Sarah-Jean Meyer
2752048 Studentship EP/S023925/1 30/09/2022 29/09/2026 Tianyi Liu
2748008 Studentship EP/S023925/1 30/09/2022 29/09/2026 Holly Chambers
2766515 Studentship EP/S023925/1 01/01/2023 31/12/2026 Zihao Shen
2891809 Studentship EP/S023925/1 29/09/2023 29/09/2027 Chek Lau
2879303 Studentship EP/S023925/1 30/09/2023 29/09/2027 Matthieu Meunier
2879315 Studentship EP/S023925/1 30/09/2023 29/09/2027 Peter Paulovics
2891810 Studentship EP/S023925/1 30/09/2023 29/09/2027 Francesco Piatti
2879265 Studentship EP/S023925/1 30/09/2023 29/09/2027 Luca Bonengel
2879285 Studentship EP/S023925/1 30/09/2023 29/09/2027 Riya Danait
2879337 Studentship EP/S023925/1 30/09/2023 29/09/2027 Edward Tansley
2879302 Studentship EP/S023925/1 30/09/2023 29/09/2027 Liam Hill
2891685 Studentship EP/S023925/1 30/09/2023 29/09/2027 Emilia Gibson
2879273 Studentship EP/S023925/1 30/09/2023 29/09/2027 Sergio Calvo Ordonez
2879300 Studentship EP/S023925/1 30/09/2023 29/09/2027 Zihan Guo
2893308 Studentship EP/S023925/1 30/09/2023 29/09/2027 Konrad Mueller
2891657 Studentship EP/S023925/1 30/09/2023 29/09/2027 Michal Fedorowicz
2891701 Studentship EP/S023925/1 30/09/2023 29/09/2027 Sturmius Tuschmann
2893386 Studentship EP/S023925/1 30/09/2023 29/09/2027 Christopher Chalhoub
2879317 Studentship EP/S023925/1 30/09/2023 29/09/2027 Yuantao Shi
2879299 Studentship EP/S023925/1 30/09/2023 29/09/2027 Mie Gluckstad
2879290 Studentship EP/S023925/1 30/09/2023 29/09/2027 Danilo Jr Dela Cruz
2891750 Studentship EP/S023925/1 30/09/2023 29/09/2027 David Fox
2879334 Studentship EP/S023925/1 30/09/2023 29/09/2027 Wen Su
2879375 Studentship EP/S023925/1 30/09/2023 29/09/2027 Thomas Blore
2879343 Studentship EP/S023925/1 30/09/2023 29/09/2027 Vlad Tuchilus
2879260 Studentship EP/S023925/1 30/09/2023 29/09/2027 Muhammad Aqsha
2891743 Studentship EP/S023925/1 30/09/2023 29/09/2027 Robert Boyce