This Centre for Doctoral training in Industrially Focused Mathematical Modelling will train the next generation of applied mathematicians to fill critical roles in industry and academia. Complex industrial problems can often be addressed, understood, and mitigated by applying modern quantitative methods. To effectively and efficiently apply these techniques requires talented mathematicians with well-practised problem-solving skills. They need to have a very strong grasp of the mathematical approaches that might need to be brought to bear, have a breadth of understanding of how to convert complex practical problems into relevant abstract mathematical forms, have knowledge and skills to solve the resulting mathematical problems efficiently and accurately, and have a wide experience of how to communicate and interact in a multidisciplinary environment. This CDT has been designed by academics in close collaboration with industrialists from many different sectors. Our 35 current CDT industrial partners cover the sectors of: consumer products (Sharp), defence (Selex, Thales), communications (BT, Vodafone), energy (Amec, BP, Camlin, Culham, DuPont, GE Energy, Infineum, Schlumberger x2, VerdErg), filtration (Pall Corp), finance (HSBC, Lloyds TSB), food and beverage (Nestle, Mondelez), healthcare (e-therapeutics, Lein Applied Diagnostics, Oxford Instruments, Siemens, Solitonik), manufacturing (Elkem, Saint Gobain), retail (dunnhumby), and software (Amazon, cd-adapco, IBM, NAG, NVIDIA), along with two consultancy companies (PA Consulting, Tessella) and we are in active discussion with other companies to grow our partner base. Our partners have five key roles: (i) they help guide and steer the centre by participating in an Industrial Engagement Committee, (ii) they deliver a substantial elements of the training and provide a broad exposure for the cohorts, (iii) they provide current challenges for our students to tackle for their doctoral research, iv) they give a very wide experience and perspective of possible applications and sectors thereby making the students highly flexible and extremely attractive to employers, and v) they provide significant funding for the CDT activities. Each cohort will learn how to apply appropriate mathematical techniques to a wide range of industrial problems in a highly interactive environment. In year one, the students will be trained in mathematical skills spanning continuum and discrete modelling, and scientific computing, closely integrated with practical applications and problem solving. The experience of addressing industrial problems and understanding their context will be further enhanced by periods where our partners will deliver a broad range of relevant material. Students will undertake two industrially focused mini-projects, one from an academic perspective and the other immersed in a partner organisation. Each student will then embark on their doctoral research project which will allow them to hone their skills and techniques while tackling a practical industrial challenge. The resulting doctoral students will be highly sought after; by industry for their flexible and quantitative abilities that will help them gain a competitive edge, and by universities to allow cutting-edge mathematical research to be motivated by practical problems and be readily exploitable.

What accurately describes such real-world processes as fluid flow mechanisms, or chemical reactions for the manufacture of industrial products? What mathematical formalism enables practitioners to guarantee a specific physical behaviour or motion of a fluid, or to maximise the yield of a particular substance? The answer lies in the important scientific field of PDE-constrained optimisation. PDEs are mathematical tools called partial differential equations. They enable us to model and predict the behaviour of a wide range of real-world physical systems. From the optimisation point-of-view, a particularly important set of such problems are those in which the dynamics may be controlled in some desirable way, for instance by applying forces to a domain in which fluid flow takes place, or inserting chemical reactants at certain rates. By influencing a system in this way, we are able to generate an optimised outcome of a real-world process. It is hence essential to study and understand PDE-constrained optimisation problems. The possibilities offered by such problems are immense, influencing groundbreaking research in applied mathematics, engineering, and the experimental sciences. Crucial real-world applications for such problems arise in fluid dynamics, chemical and biological mechanisms, weather forecasting, image processing including medical imaging, financial markets and option pricing, and many others. Although a great deal of theoretical work has been undertaken for such problems, it has only been in the past decade or so that a focus has been placed on solving them accurately and robustly on a computer, by tackling the matrix systems of equations which result. Much of the research underpinning this proposal involves constructing powerful iterative methods accelerated by 'preconditioners', which are built by approximating the relevant matrix in an accurate way, such that the preconditioner is much cheaper to apply than solving the matrix system itself. Applying our methodology can then open the door to scientific challenges which were previously out of reach, by only storing and working with matrices that are tiny compared to the systems being solved overall. Recently, PDE-constrained optimisation problems have found crucial applicability to problems from data analysis. This is due to the vast computing power that is available today, meaning that there exists the potential to store and work with huge-scale datasets arising from commercial records, online news sites, or health databases, for example. In turn, this has led to a number of applications of data-driven processes being successfully modelled by optimisation problems constrained by PDEs. It is essential that algorithms for solving problems from these applications of data science can keep pace with the explosion of data which arises from real-world processes. Our novel numerical methods for solving the resulting huge-scale matrix systems aim to do exactly this. In this project, we will examine PDE-constrained optimisation problems under the presence of uncertain data, image processing problems, bioinformatics applications, and deep learning processes. For each problem, we will devise state-of-the-art mathematical models to describe the process, for which we will then construct potent iterative solvers and preconditioners to tackle the resulting matrix systems. Our new algorithms will be validated theoretically and numerically, whereupon we will then release an open source code library to maximise their applicability and impact on modern optimisation and data science problems.

Research in Particle Physics (PP) in the next decade will be dominated by a 10x increase in the amount of experimental data, leading to unprecedented precision. Analysing and interpreting these data requires advanced simulation techniques and is an important use-case for Exascale computing worldwide. This project aims to develop novel algorithms and paradigms for large scale simulations to maximise the performance extracted from heterogeneous parallel hardware architectures that are being deployed at large HPC centres across the world. The ExaTEPP proposal puts the particle physics use-case at the centre of the ExCALIBUR programme, through the use of existing and future testbeds and the collaboration and exchange of ideas with other working groups. Our goal is to develop the tools needed in the UK to exploit HPC in the next decade and to focus on the transferable skills acquired by RSEs working on this use-case. Research projects in both theoretical and experimental particle physics are based on large international collaborations, and collaborative values are deeply embedded in the research culture of the field. ExaTEPP is built upon existing international collaborations with the goal of providing world-leading contributions to future developments. Collaboration with industry is crucial to gain and exchange technical knowledge and fully exploit advancements in both hardware and software. Leading HPC industries have endorsed the activities of ExaTEPP, committing representatives of theirs to actively contribute to our programme and to the management board of the project in order to foster a dynamic, bidirectional knowledge exchange. The activities of ExaTEPP are strongly aligned with the four pillars of the ExCALIBUR programme. While delivering the new software needed by the community, ExaTEPP will contribute directly to advance the ExCALIBUR goals, integrate with cross-cutting themes and exploit the available hardware testbeds for software optimisation. The proposal is structured into three work packages (WP). WP1 focuses on training, knowledge exchange and communication with other ExCALIBUR working groups representing other scientific disciplines in the UK. WP2 focuses on development of simulations on HPCs as an essential tool to address urgent particle physics questions that dominate the international research landscape and are highly relevant for UK science, such as the nature of the Higgs boson or the understanding of the muon gyromagnetic factor (g-2). Benchmarking work is proposed in WP3 to monitor the efficiency of the software developed to maximise the physics output per kWh of power, contributing to the decarbonisation agenda. Our work will primarily impact the scientific community, both in our specific fields and more broadly in high-performance scientific computing, including the wider ExCALIBUR programme, and the supercomputing industry. Our outputs will be disseminated in the PP scientific community through participation in conferences, organisation of workshops and training events, and scientific publications in highly reputed journals. To promote and disseminate the code and the material that we shall develop, we will open events such as hackathons and schools to other ExCALIBUR funded working groups, to industry and to the wider community. Contributions to already open-source software will be made available following the development processes for each project; new projects will be made available as open source through publicly accessible repositories (e.g., GitHub), and we will work with the authors of any currently proprietary software touched by the project to enable them to open-source their projects. The training material will similarly be freely licensed and made available on dedicated open web sites and YouTube channels.

"Software is the most prevalent of all the instruments used in modern science" [Goble 2014]. Scientific software is not just widely used [SSI 2014] but also widely developed. Yet much of it is developed by researchers who have little understanding of even the basics of modern software development with the knock-on effects to their productivity, and the reliability, readability and reproducibility of their software [Nature Biotechnology]. Many are long-tail researchers working in small groups - even Big Science operations like the SKA are operationally undertaken by individuals collectively. Technological development in software is more like a cliff-face than a ladder - there are many routes to the top, to a solution. Further, the cliff face is dynamic - constantly and quickly changing as new technologies emerge and decline. Determining which technologies to deploy and how best to deploy them is in itself a specialist domain, with many features of traditional research. Researchers need empowerment and training to give them confidence with the available equipment and the challenges they face. This role, akin to that of an Alpine guide, involves support, guidance, and load carrying. When optimally performed it results in a researcher who knows what challenges they can attack alone, and where they need appropriate support. Guides can help decide whether to exploit well-trodden paths or explore new possibilities as they navigate through this dynamic environment. These guides are highly trained, technology-centric, research-aware individuals who have a curiosity driven nature dedicated to supporting researchers by forging a research software support career. Such Research Software Engineers (RSEs) guide researchers through the technological landscape and form a human interface between scientist and computer. A well-functioning RSE group will not just add to an organisation's effectiveness, it will have a multiplicative effect since it will make every individual researcher more effective. It has the potential to improve the quality of research done across all University departments and faculties. My work plan provides a bottom-up approach to providing RSE services that is distinctive from yet complements the top-down approach provided by the EPRSC-funded Software Sustainability Institute. The outcomes of this fellowship will be: Local and National RSE Capability: A RSE Group at Sheffield as a credible roadmap for others pump-priming a UK national research software capability; and a national Continuing Professional Development programme for RSEs. Scalable software support methods: A scalable approach based on "nudging", to providing research software support for scientific software efficiency, sustainability and reproducibility, with quality-guidelines for research software and for researchers on how best to incorporate research software engineering support within their grant proposals. HPC for long-tail researchers: 'HPC-software ramps' and a pathway for standardised integration of HPC resources into Desktop Applications fit for modern scientific computing; a network of HPC-centric RSEs based around shared resources; and a portfolio of new research software courses developed with partners. Communication and public understanding: A communication campaign to raise the profile of research software exploiting high profile social media and online resources, establishing an informal forum for research software debate. References [Goble 2014] Goble, C. "Better Software, Better Research". IEEE Internet Computing 18(5): 4-8 (2014) [SSI 2014] Hettrick, S. "It's impossible to conduct research without software, say 7 out of 10 UK researchers" http://www.software.ac.uk/blog/2014-12-04-its-impossible-conduct-research-without-software-say-7-out-10-uk-researchers (2014) [Nature 2015] Editorial "Rule rewrite aims to clean up scientific software", Nature Biotechnology 520(7547) April 2015