EPSRC Centre for Doctoral Training in Mathematics for Real-World Systems II

We propose a new phase of the successful Mathematics for Real-World Systems (MathSys) Centre for Doctoral Training that will address the call priority area "Mathematical and Computational Modelling".

Advanced quantitative skills and applied mathematical modelling are critical to address the contemporary challenges arising from biomedicine and health sectors, modern industry and the digital economy. The UK Commission for Employment and Skills as well as Tech City UK have identified that a skills shortage in this domain is one of the key challenges facing the UK technology sector: there is a severe lack of trained researchers with the technical skills and, importantly, the ability to translate these skills into effective solutions in collaboration with end-users.

Our proposal addresses this need with a cross-disciplinary, cohort-based training programme that will equip the next generation of researchers with cutting-edge methodological toolkits and the experience of external end-user engagement to address a broad variety of real-world problems in fields ranging from mathematical biology to the high-tech sector. Our MSc training (and continued PhD development) will deliver a core of mathematical techniques relevant to all applied modelling, but will also focus on two cross-cutting methodological themes which we consider key to complex multi-scale systems prediction: modelling across spatial and temporal scales; and hybrid modelling integrating complex data and mechanistic models. These themes pervade many areas of active research and will shape mathematical and computational modelling for the coming decades.

A core element of the CDT will be productive and impactful engagement with end-users throughout the teaching and research phases. This has been a distinguishing feature of the MathSys CDT and is further expanded in our new proposal. MSc Research Study Groups provide an ideal opportunity for MSc students to experience working in a collaborative environment and for our end-users to become actively involved. All PhD projects are expected to be co-supervised by an external partner, bringing knowledge, data and experience to the modelling of real-world problems; students will normally be expected to spend 2-4 weeks (or longer) with these end-users to better understand the case-specific challenges and motivate their research. The potential renewal of the MathSys CDT has provided us with the opportunity to expand our portfolio of external partners focusing on research challenges in four application areas: Quantitative biomedical research, (A2) Mathematical epidemiology, (A3) Socio-technical systems and (A4) Advanced modelling and optimization of industrial processes.

We will retain the one-year MSc followed by three-year PhD format that has been successfully refined through staff experience and student feedback over more than a decade of previous Warwick doctoral training centres. However, both the training and research components of the programme will be thoroughly updated to reflect the evolving technical landscape of applied research and the changing priorities of end-users. At the same time, we have retained the flexibility that allows co-creation of activities with our end-users and allows us to respond to changes in the national and international research environments on an ongoing yearly basis.

Students will share a dedicated space, with a lecture theatre and common area based in one of the UK's leading mathematical departments. The space is physically connected to the new Mathematical Sciences building, at the interface of Mathematics, Statistics and Computer Science, and provides a unique location for our interdisciplinary activities.

In the 2018 Government Office for Science report, 'Computational Modelling: Technological Futures', Greg Clarke, the Secretary of State for Business Energy and Industrial Strategy, wrote "Computational modelling is essential to our future productivity and competitiveness, for businesses of all sizes and across all sectors of the economy". With its focus on computational models, the mathematics that underpin them, and their integration with complex data, the MathSys II CDT will generate diverse impacts beyond academia. This includes impacts on skills, on the economy, on policy and on society.

Impacts on skills.
MathSys II will produce a minimum of 50 PhD graduates to support the growing national demand for advanced mathematical modelling and data analysis skills. The CDT will provide each of them with broad core skills in the MSc, a deep knowledge of their chosen research specialisation in the PhD and a complementary qualification in transferable skills integrated throughout. Graduates will thus acquire the profiles needed to form the next generation of leaders in business, government and academia. They will be supported by an integrated pastoral support framework, including a diverse group of accessible leadership role models. The cohort based environment of the CDT provides a multiplier effect by encouraging cohorts to forge long-lasting professional networks whose value and influence will long outlast the CDT itself. MathSys II will seek to maximise the influence of these networks by providing topical training in Responsible Research and Innovation, by maintaining a robust Equality, Diversity & Inclusion policy, and by integration with Warwick's global network of international partnerships.

Economic impacts.
The research outputs from many MathSys II PhD projects will be of direct economic value to commercial, public sector and charitable external partners. Engagement with CDT partners will facilitate these impacts. This includes co-supervision of PhD and MSc projects, co-creation of Research Study Groups, and a strong commitment to provide placements/internships for CDT students. When commercial innovations or IP are generated, we will work with Warwick Ventures, the commercial arm of the University of Warwick, to commercialise/license IP where appropriate. Economic impact may also come from the creation of new companies by CDT graduates. MathSys II will present entrepreneurship as a viable career option to students. One external partner, Spectra Analytics, was founded by graduates of the preceding Complexity Science CDT, thus providing accessible role models. We will also provide in-house entrepreneurship training via Warwick Ventures and host events by external start-up accelerator Entrepreneur First.

Impacts on policy.
The CDT will influence policy at the national and international level by working with external partners operating in policy. UK examples include Department of Health, Public Health England and DEFRA. International examples include World Health Organisation (WHO) and the European Commission for the Control of Foot-and-mouth Disease (EuFMD). MathSys students will also utilise the recently announced UKRI policy internships scheme.

Impacts on society.
Public engagement will allow CDT students to promote the value of their research to society at large. Aside from social media, suitable local events include DataBeers, Cafe Scientifique, and the Big Bang Fair. MathSys will also promote a socially-oriented ethos of technology for the common good. Concretely, this includes the creation of open-source software, integration of software and data carpentry into our computational and data driven research training and championing open-access to research. We will also contribute to the 'innovation culture and science' strand of Coventry's 2021 City of Culture programme.