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.

Chemistry impacts most areas of our lives, including healthcare, energy production, and the environment. It is also the UK's second largest manufacturing industry, employing 140,00 people. This hub will bring the transformative power of artificial intelligence (AI) to the area of chemistry, and by doing so have a major societal impact. Both AI and chemistry are fast-moving and historically separated research disciplines, and there is huge untapped potential to collaborate at the interface of these two fields. Today, relatively few UK experimental chemists are exploiting AI (e.g., for reaction optimization), and few have corresponding automation facilities to do this, which is a missed opportunity. The use of machine learning methods is more common in computational chemistry, but here also we are often data poor, and data is sparse. In some AI fields, such as natural language processing, there is also rapidly evolving, leading-edge industrial research, necessitating a cross-sector approach if we are to exploit the cutting edge of this technology. This hub (AIchemy) will bring together leading researchers in AI and trailblazers at the interface of AI for chemistry, spanning both university and industry. We will exploit unique established facilities and institutes in the four core partner institutions (Universities of Liverpool, Imperial, Cambridge, and Southampton) where cross-discipline working has already been achieved: this includes the Materials Innovation Factory (MIF), the Institute for Digital Molecular Design and Fabrication (DigiFAB), and the I-X Centre for AI in Science. In addition to the 6 lead investigators, we have aligned 25 other investigators across nine institutions, spanning the areas of AI, robotics, and a diverse range of experimental and computational chemistry sub-disciplines, and career stages. The team also includes unique expertise in robotics and automation (Liverpool & Imperial), natural language processing for chemistry problems (Cambridge) and data curation in the Physical Sciences Data Infrastructure (PSDI, Southampton). This diverse team and associated facilities give us the breadth of expertise and critical mass to become the core of a UK hub for this activity. AIchemy will carry out world-leading research at the AI/chemistry interface, building on distinctive UK strengths in this area and developed initially via 6 Forerunner Projects. The Hub will also build an approach for sharing chemistry research data and code in a common format to unite the currently fragmented UK research landscape. We also aim to dramatically broaden the number of AI researchers tackling chemistry problems, and vice versa, through a mixture of pump-priming funding in the hub, bespoke training, access to datasets, and events (e.g., AI challenges using hub-generated data). To ensure the long-term health of this discipline, we will also focus resource on projects that are led by early career academics. The hub will build a UK-wide consortium involving university and industry stakeholders outside of the core partners, including a broad set of 15 day-one industry partners across the sectors of AI and chemistry, to be further expanded in the full proposal. The team has an excellent collective track record in industry engagement and knowledge transfer; e.g. MIF collocates 100 industry researchers in a common facility with academics; Chemistry is co-located with IX at Imperial's £2 Bn White City campus, and there are shared spaces to enable 800 scientists and industry partners to work together on common challenges, with tailor-made labs and offices for early stage companies. Mirroring the enormous benefits that have been achieved in other science areas, such as structural biology, this hub will transform the UK landscape for the discipline of chemistry, transforming engagement with AI from a relatively niche activity to a core, platform methodology.