The proposed programme of research will establish the machine learning foundations and artificial intelligence methodologies for Digital Twins. Digital Twins are digital representations of real-world physical phenomena and assets, that are coupled with the corresponding physical twin through instrumentation and live data and information flows. This research programme will establish next-generation Digital Twins that will enable decision makers to perform accurate but simulated "what-if" scenarios in order to better understand the real world phenomena and improve overall decision making and outcomes.

Nature-based solutions (NbS*) are responses to societal challenges that involve working with nature to deliver benefits for both people and biodiversity. They include protecting existing ecosystems, restoring degraded ecosystems and managing working lands more sustainably. NbS are of national strategic importance in supporting the UK's net zero climate targets and the Government's ambition to improve the environment within a generation. They have gained international significance too: 131 countries include NbS in their UNFCCC climate change pledges. If well designed and robustly implemented, NbS will deliver multiple benefits for climate change mitigation and adaptation, enhance biodiversity, promote human wellbeing and support economic recovery. The challenge is that the implementation of NbS is often piecemeal, narrow in focus, and undermined by weak research/policy/practice connections. UCam-Regen will redress this problem by applying its breadth of expertise in a practically driven analysis that provides the knowledge and tools needed to address several challenges facing the delivery of NbS: NbS can contribute significantly to achieving net zero emissions, although the extent of that contribution is limited by the finite amount of land available and critically by the effects of climate change on ecosystems. NbS are not an alternative to decarbonising the economy and must be accompanied by swift, deep emissions cuts; they must be designed with and for local communities; and they must deliver measurable benefits for biodiversity and be designed to be resilient to climate change i.e. a 'whole systems approach' must be applied - as in UCam-Regen - that integrates economies, societies, and nature. Scaling up, restoration and protection of key ecosystems across UK landscapes requires (a) better protection of natural habitats in the planning system; (b) reforming agriculture and forestry subsidies to better support actions that benefit both climate regulation and biodiversity; (c) connecting habitats across landscapes, building on the emerging Nature Recovery Networks; (d) making it compulsory to build an NbS framework into all new developments, and (e) making space on land for natural systems to adapt to climate change. There is a need to develop robust metrics to assess the effectiveness of a wide range of NbS for carbon sequestration, water regulation, biodiversity and human wellbeing. Well-designed new financing mechanisms, including tax incentives and public subsidies for ecosystem stewardship that meet the NbS guidelines and support climate change mitigation, climate change adaptation and biodiversity, could be instrumental for upscaling NbS and improving social-ecological resilience to climate change, both in the UK and globally. UCam-Regen addresses these challenges by applying a whole systems approach to deliver knowledge and tools necessary to regenerate UK landscapes using NbS approaches. At the heart of the proposal is a recognition that local communities must be engaged with decisions regarding their landscape's future and co-produce solutions, informed by scientific assessments of the optimal landscape management approaches to maximise the delivery of ecosystem services. *We take policy recommendation and definitions from a COP26 Universities Network Briefing led by Prof Coomes https://www.gla.ac.uk/media/Media_790171_smxx.pdf

The CDT will train the next generation of leaders in statistics and statistical machine learning, who will be able to develop widely-applicable novel methodology and theory, as well as create application-specific methods, leading to breakthroughs in real-world problems in government, medicine, industry and science. The research will focus on the development of applicable modern statistical theory and methods as well as on the underpinnings of statistical machine learning. The research will be strongly linked to applications. There is an urgent national need for graduates from this CDT. Large volumes of complicated data are now routinely collected in all sectors of society, encompassing electronic health records, massive scientific datasets, governmental data, and data collected through the advent of the digital economy. The underpinning techniques for exploiting these data come from statistics and machine learning. Exploiting such data is crucial for future UK prosperity. However, several reports from government and learned societies have identified a lack of individuals able to exploit this data. In many situations, existing methodology is insufficient. Off-the-shelf approaches may be misleading due to a lack of reproducibility or sampling biases which they do not correct. Furthermore, understanding the underlying mechanisms is often desired: scientifically valid, interpretable and reproducible results are needed to understand scientific phenomena and to justify decisions, particularly those affecting individuals. Bespoke, model-based statistical methods are needed, that may need to be blended with statistical machine learning approaches to deal with large data. Individuals that can fulfill these more sophisticated demands are doctoral level graduates in statistics who are well versed in the foundations of machine learning. Yet the UK only graduates a small number of statistics PhDs per year, and many of these graduates will not have been exposed to machine learning. The Centre will bring together Imperial and Oxford, two top statistics groups, as equal partners, offering an exceptional training environment and the direct involvement of absolute research leaders in their fields. The supervisor pool will include outstanding researchers in statistical methodology and theory as well as in statistical machine learning. We will use innovative and student-led teaching, focussing on PhD-level training. Teaching cuts across years and thus creates strong cohort cohesion not just within a year group but also between year groups. We will link theoretical advances to application areas through partner interactions as well as through a placement of students with users of statistics. The CDT has a large number of high profile partners that helped shape our application priority areas (digital economy, medicine, engineering, public health, science) and that will co-fund and co-supervise PhD students, as well as co-deliver teaching elements.