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.

The Centre for Doctoral Training MAC-MIGS will provide advanced training in the formulation, analysis, and implementation of state-of-the-art mathematical and computational models. The vision for the training offered is that effective modern modelling must integrate data with laws framed in explicit, rigorous mathematical terms. The CDT will offer 76 PhD students an intensive 4-year training and research programme that equips them with the skills needed to tackle the challenges of data-intensive modelling. The new generation of successful modelling experts will be able to develop and analyse mathematical models, translate them into efficient computer codes that make best use of available data, interpret the results, and communicate throughout the process with users in industry, commerce and government. Mathematical and computational models are at the heart of 21st-century technology: they underpin science, medicine and, increasingly, social sciences, and impact many sectors of the economy including high-value manufacturing, healthcare, energy, physical infrastructure and national planning. When combined with the enormous computing power and volume of data now available, these models provide unmatched predictive tools which capture systematically the experimental and observational evidence available. Because they are based on sound deductive principles, they are also the only effective tool in many problems where data is either sparse or, as is often the case, acquired in conditions that differ from the relevant real-world scenarios. Developing and exploiting these models requires a broad range of skills - from abstract mathematics to computing and data science - combined with expertise in application areas. MAC-MIGS will equip its students with these skills through a broad programme that cuts across disciplinary boundaries to include mathematical analysis - pure, applied, numerical and stochastic - data-science and statistics techniques and the domain-specific advanced knowledge necessary for cutting-edge applications. MAC-MIGS students will join the broader Maxwell Institute Graduate School in its brand-new base located in central Edinburgh. They will benefit from (i) dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning; (ii) extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships; (iii) outstanding early-career training, with a strong focus on entrepreneurship; and (iv) a dynamic and forward-looking community of mathematicians and scientists, sharing strong values of collaboration, respect, and social and scientific responsibility. The students will integrate a vibrant research environment, closely interacting with some 80 MAC-MIGS academics comprised of mathematicians from the universities of Edinburgh and Heriot-Watt as well as computer scientists, engineers, physicists and chemists providing their own disciplinary expertise. Students will benefit from MAC-MIGS's diverse network of more than 30 industrial and agency partners spanning a broad spectrum of application areas: energy, engineering design, finance, computer technology, healthcare and the environment. These partners will provide internships, development programmes and research projects, and help maximise the impact of our students' work. Our network of academic partners representing ten leading institutions in the US and Europe, will further provide opportunities for collaborations and research visits.

Soft matter and functional interfaces are ubiquitous! Be it manufactured plastic products (polymers), food (colloids), paint and other decorative coatings (thin films and coatings), contact lenses (hydrogels), shampoo and washing powder (complex mixtures of the above) or biomaterials such as proteins and membranes, soft matter and soft matter surfaces and interfaces touch almost every aspect of human activity and underpin processes and products across all industrial sectors - sectors which account for 17.2% of UK GDP and over 1.1M UK employees (BIS R&D scoreboard 2010 providing statistics for the top 1000 UK R&D spending companies). The importance of the underlying science to UK plc prompted discussions in 2010 with key manufacturing industries in personal care, plastics manufacturing, food manufacturing, functional and performance polymers, coatings and additives sectors which revealed common concerns for the provision of soft matter focussed doctoral training in the UK and drove this community to carry out a detailed "gap analysis" of training provision. The results evidenced a national need for researchers trained with a broad, multidisciplinary experience across all areas of soft matter and functional interfaces (SOFI) science, industry-focussed transferable skills and business awareness alongside a challenging PhD research project. Our 18 industrial partners, who have a combined global work force of 920,000, annual revenues of nearly £200 billion, and span the full SOFI sector, emphasized the importance of a workforce trained to think across the whole range of SOFI science, and not narrowly in, for example, just polymers or colloids. A multidisciplinary knowledge base is vital to address industrial SOFI R&D challenges which invariably address complex, multicomponent formulations. We therefore propose the establishment of a CDT in Soft Matter and Functional Interfaces to fill this gap. The CDT will deliver multidisciplinary core science and enterprise-facing training alongside PhD projects from fundamental blue-skies science to industrially-embedded applied research across the full spectrum of SOFI science. Further evidence of national need comes from a survey of our industrial partners which indicates that these companies have collectively recruited >100 PhD qualified staff over the last 3 years (in a recession) in SOFI-related expertise, and plan to recruit (in the UK) approximately 150 PhD qualified staff members over the next three years. These recruits will enter research, innovation and commercial roles. The annual SOFI CDT cohort of 16 postgraduates could be therefore be recruited 3 times over by our industrial partners alone and this demand is likely to be the tip of a national-need iceberg.

Developing and improving our R&D and manufacturing capabilities to prepare greater numbers of higher quality crystalline materials has become a growing societal and hence industrial need. This requires higher levels of precision and speed throughout the R&D development cycle to meet the evolving needs for precision crystals in fine chemical's sector such as for pharmaceuticals, agrochemicals and additives. For example, a more differentiated product range is expected to be produced with a significantly faster molecule to patient journey, in much smaller volumes and at significantly lower costs. For pharmaceuticals, this will provide a wider range of more targeted medicines and dosage forms, ensuring the delivery of patient-targeted dosage forms with much improved safety and efficacy, hence enormously benefiting economy, environment and society. Such an increase in the multiplicity of crystalline products demands the implementation of digitally-enabled and AI technologies as highlighted in UK government policy and global initiatives. The surface properties of crystals are very important for the digital design and manufacture of precision particles via solution crystallisation. Control of the surfaces expressed on crystalline particles represents a critical objective for the fine chemical industry which manufactures ca. 70% of their ingredients in solid (crystalline) form. These crystals have their unique shapes and surface chemistry which, when variable, can impact adversely upon product quality and performance. Specifically, the effective digital design of such products and the associated processes for their manufacture demands a detailed knowledge of surface properties of the product's formulation ingredients. Currently there exists a critical gap to relate the measurable properties at the molecular and single crystal levels to the behaviour and performance of the same material when it is manufactured or used in particulate form. This perspective demands the development of a digitally-enabled platform which is able to characterise, monitor and control crystal size and shape. However, existing crystal shape descriptors available with current commercial particle measurement systems have limited capabilities and the corresponding algorithms tend, unrealistically, to be based upon the assumption that non-spherical crystals can be treated as spherical ones. Therefore, the development of advanced process-inspired analytical tools, particularly of AI-based approach, combining with first-principle, shape-based models are clearly needed. Such approaches are important in order to ensure that the UK's research-led fine chemical and pharmaceutical industry continues to provide outstanding international leadership in product development and manufacture so maintaining and enhancing its global competitiveness. The proposed research will apply machine learning based upon crystal morphology prediction (forward engineering) to map from 2D in-process microscopy data back to a description of a crystal's 3D shape (reverse engineering) and, through this, to its functional surface properties. This will enable the design and control of more efficient and agile manufacturing processes for crystalline fine chemicals, delivering precision crystals with a much tighter specification in terms of their size and shape than is currently feasible, hence resulting in products having more consistency, less variability, higher quality. The outcomes will be a digital platform of crystal shape characterisation and process dynamics control for precision particle manufacture. The approach developed will be shared through academic collaboration (such as the CMAC Hub, INFORM2020, Cambridge Crystallographic Data Centre, Imperial College etc.) and with industry (Infineum, Keyence, Pfizer, Roche, Syngenta etc.) and also extended in due course more widely, expecting potentially enormous economic and societal impact.