PREMIERE will integrate challenges identified by the EPSRC Prosperity Outcomes and the Industrial Strategy Challenge Fund (ISCF) in healthcare (Healthy Nation), energy (Resilient Nation), manufacturing and digital technologies (Resilient Nation, Productive Nation) as areas to drive economic growth. The programme will bring together a multi-disciplinary team of researchers to create unprecedented impact in these sectors through the creation of a next-generation predictive framework for complex multiphase systems. Importantly, the framework methodology will span purely physics-driven, CFD-mediated solutions at one extreme, and data-centric solutions at the other where the complexity of the phenomena masks the underlying physics. The framework will advance the current state-of-the-art in uncertainty quantification, adjoint sensitivity, data-assimilation, ensemble methods, CFD, and design of experiments to 'blend' the two extremes in order to create ultra-fast multi-fidelity, predictive models, supported by cutting-edge experimental investigations. This transformative technology will be sufficiently generic so as to address a wide spectrum of challenges across the ISCF areas, and will empower the user with optimal compromises between off-line (modelling) and on-line (simulation) efforts so as to meet an a priori 'error bar' on the model outputs. The investigators' synergy, and their long-standing industrial collaborations, will ensure that PREMIERE will result in a paradigm-shift in multiphase flow research worldwide. We will demonstrate our capabilities using exemplar challenges, of central importance to their respective sectors in close collaboration with our industrial and healthcare partners. Our PREMIERE framework will provide novel and more efficient manufacturing processes, reliable design tools for the oil-and-gas industry, which remove conservatism in design, improve safety management, and reduce emissions and carbon footprint. This framework will also provide enabling technology for the design, operation, and optimisation of the next-generation nuclear reactors, and associated reprocessing, as well as patient-specific therapies for diseases such as acute compartment syndrome.

The international offshore energy industry is undergoing as revolution, adopting aggressive net-zero objectives and shifting rapidly towards large scale offshore wind energy production. This revolution cannot be done using 'business as usual' approaches in a competitive market with low margins. Further, the offshore workforce is ageing as new generations of suitable graduates prefer not to work in hazardous places offshore. Operators therefore seek more cost effective, safe methods and business models for inspection, repair and maintenance of their topside and marine offshore infrastructure. Robotics and artificial intelligence are seen as key enablers in this regard as fewer staff offshore reduces cost, increases safety and workplace appeal. The long-term industry vision is thus for a digitised offshore energy field, operated, inspected and maintained from the shore using robots, digital architectures and cloud based processes to realise this vision. In the last 3 years, we has made significant advances to bring robots closer to widespread adoption in the offshore domain, developing close ties with industrial actors across the sector. The recent pandemic has highlighted a widespread need for remote operations in many other industrial sectors. The ORCA Hub extension is a one year project from 5 UK leading universities with over 20 industry partners (>£2.6M investment) which aims at translating the research done into the first phase of the Hub into industry led use cases. Led by the Edinburgh Centre of Robotics (HWU/UoE), in collaboration with Imperial College, Oxford and Liverpool Universities, this multi-disciplinary consortium brings its unique expertise in: Subsea (HWU), Ground (UoE, Oxf) and Aerial robotics (ICL); as well as human-machine interaction (HWU, UoE), innovative sensors for Non Destructive Evaluation and low-cost sensor networks (ICL, UoE); and asset management and certification (HWU, UoE, LIV). The Hub will provide remote solutions using robotics and AI that are applicable across a wide range of industrial sectors and that can operate and interact safely in autonomous or semi-autonomous modes in complex and cluttered environments. We will develop robotics solutions enabling accurate mapping , navigation around and interaction with assets in the marine, aerial and ground environments that support the deployment of sensors for asset monitoring. This will be demonstrated using 4 industry led use cases developed in close collaboration with our industry partners and feeding directly into their technology roadmaps: Offshore Renewable Energy Subsea Inspection in collaboration with EDF, Wood, Fugro, OREC, Seebyte Ltd and Rovco; Aerial Inspection of Large Infrastructures in Challenging Conditions in collaboration with Barrnon, BP, Flyability, SLAMCore, Voliro and Helvetis; Robust Inspection and Manipulation in Hazardous Environments in collaboration with ARUP, Babcock, Chevron, EMR, Lafarge, Createc, Ross Robotics; Symbiotic Systems for Resilient Autonomous Missions in collaboration with TLB, Total Wood and the Lloyds Register. This will see the Hub breach into new sectors and demonstrate the potential of our technology on a wider scale.

SAMBa aims to create a generation of interdisciplinary mathematicians at the interface of stochastics, numerical analysis, applied mathematics, data science and statistics, preparing them to work as research leaders in academia and in industry in the expanding world of big models and big data. This research spectrum includes rapidly developing areas of mathematical sciences such as machine learning, uncertainty quantification, compressed sensing, Bayesian networks and stochastic modelling. The research and training engagement also encompasses modern industrially facing mathematics, with a key strength of our CDT being meaningful and long term relationships with industrial, government and other non-academic partners. A substantial proportion of our doctoral research will continue to be developed collaboratively through these partnerships. The urgency and awareness of the UK's need for deep quantitative analytical talent with expert modelling skills has intensified since SAMBa's inception in 2014. Industry, government bodies and non-academic organisations at the forefront of technological innovation all want to achieve competitive advantage through the analysis of data of all levels of complexity. This need is as much of an issue outside of academia as it is for research and training capacity within academia and is reflected in our doctoral training approach. The sense of urgency is evidenced in recent government policy (cf. Government Office for Science report "Computational Modelling, Technological Futures, 2018"), through the EPSRC CDT priority areas of Mathematical and Computational Modelling and Statistics for the 21st century as well as through our own experience of growing SAMBa since 2014. We have had extensive collaboration with partners from a wide range of UK industrial sectors (e.g. agri-science, healthcare, advanced materials) and government bodies (e.g. NHS, National Physical Laboratory, Environment Agency and Office for National Statistics) and our portfolio is set to expand. SAMBa's approach to doctoral training, developed in conjunction with our industrial partners, will create future leaders both in academia and industry and consists of: - A broad-based first year developing mathematical expertise across the full range of Statistical Applied Mathematics, tailored to each incoming student. - Deep experience in academic-industrial collaboration through Integrative Think Tanks: bespoke problem-formulation workshops developed by SAMBa. - Research training in a department which produces world-leading research in Statistical Applied Mathematics. - Multiple cohort-enhanced training activities that maximise each student's talents and includes mentoring through cross-cohort integration. - Substantial international opportunities such as academic placements, overseas workshops and participation in jointly delivered ITTs. - The opportunity for co-supervision of research from industrial and non-maths academic supervisors, including student placements in industry. This proposal will initially fund over 60 scholarships, with the aim to further increase this number through additional funding from industrial and international partners. Based on the CDT's current track record from its inception in 2014 (creating 25 scholarships to add to an initial investment of 50), our target is to deliver 90 PhD students over the next five years. With 12 new staff positions committed to SAMBa-core areas since 2015, students in the CDT cohort will benefit from almost 60 Bath Mathematical Sciences academics available for lead supervisory roles, as well as over 50 relevant co-supervisors in other departments.