Dynamic networks occur in many fields of science, technology and medicine, as well as everyday life. Understanding their behaviour has important applications. For example, whether it is to uncover serious crime on the dark web, intrusions in a computer network, or hijacks at global internet scales, better network anomaly detection tools are desperately needed in cyber-security. Characterising the network structure of multiple EEG time series recorded at different locations in the brain is critical for understanding neurological disorders and therapeutics development. Modelling dynamic networks is of great interest in transport applications, such as for preventing accidents on highways and predicting the influence of bad weather on train networks. Systematically identifying, attributing, and preventing misinformation online requires realistic models of information flow in social networks. Whilst simple random networks theory is well-established in maths and computer science, the recent explosion of dynamic network data has exposed a large gap in our ability to process real-life networks. Classical network models have led to a body of beautiful mathematical theory, but do not always capture the rich structure and temporal dynamics seen in real data, nor are they geared to answer practitioners' typical questions, e.g. relating to forecasting, anomaly detection or data ethics issues. Our NeST programme will develop robust, principled, yet computationally feasible ways of modelling dynamically changing networks and the statistical processes on them. Some aspects of these problems, such as quantifying the influence of policy interventions on the spread of misinformation or disease, require advances in probability theory. Dynamic network data are also notoriously difficult to analyse. At a computational level, the datasets are often very large and/or only available "on the stream". At a statistical level, they often come with important collection biases and missing data. Often, even understanding the data and how they may relate to the analysis goal can be challenging. Therefore, to tackle these research questions in a systematic way we need to bring probabilists, statisticians and application domain experts together. NeST's six-year programme will see probabilists and statisticians with theoretical, computational, machine learning and data science expertise, collaborate across six world-class institutes to conduct leading and impactful research. In different overlapping groups, we will tackle questions such as: How do we model data to capture the complex features and dynamics we observe in practice? How should we conduct exploratory data analysis or, to quote a famous statistician, "Looking at the data to see what it seems to say" (Tukey, 1977)? How can we forecast network data, or detect anomalies, changes, trends? To ground techniques in practice, our research will be informed and driven by challenges in many key scientific disciplines through frequent interaction with industrial & government partners in energy, cyber-security, the environment, finance, logistics, statistics, telecoms, transport, and biology. A valuable output of work will be high-quality, curated, dynamic network datasets from a broad range of application domains, which we will make publicly available in a repository for benchmarking, testing & reproducibility (responsible innovation), partly as a vehicle to foster new collaborations. We also have a strategy to disseminate knowledge through a diverse range of scientific publication routes, high-quality free software (e.g. R packages, Python notebooks accompanying data releases), conferences, patents and outreach activities. NeST will also carefully nurture and develop the next generation of highly-trained and research-active people in our area, which will contribute strongly to satisfying the high demand for such people in industry, government and academia.

The UK is world leading in Artificial Intelligence (AI) and a 2017 government report estimated that AI technologies could add £630 billion to the UK economy by 2035. However, we have seen increasing concern about the potential dangers of AI, and global recognition of the need for safe and trusted AI systems. Indeed, the latest UK Industrial Strategy recognises that there is a shortage of highly-skilled individuals in the workforce that can harness AI technologies and realise the full potential of AI. The UKRI Centre for Doctoral Training (CDT) on Safe and Trusted AI will train a new generation of scientists and engineers who are experts in model-based AI approaches and their use in developing AI systems that are safe (meaning we can provide guarantees about their behaviour) and are trusted (meaning we can have confidence in the decisions they make and their reasons for making them). Techniques in AI can be broadly divided into data-driven and model-based. While data-driven techniques (such as machine learning) use data to learn patterns or behaviours, or to make predictions, model-based approaches use explicit models to represent and reason about knowledge. Model-based AI is thus particularly well-suited to ensuring safety and trust: models provide a shared vocabulary on which to base understanding; models can be verified, and solutions based on models can be guaranteed to be correct and safe; models can be used to enhance decision-making transparency by providing human-understandable explanations; and models allow user collaboration and interaction with AI systems. In sophisticated applications, the outputs of data-driven AI may be input to further model-driven reasoning; for example, a self-driving car might use data-driven techniques to identify a busy roundabout, and then use an explicit model of how people behave on the road to reason about the actions it should take. While much current attention is focussed on recent advancements in data-driven AI, such as those from deep learning, it is crucial that we also develop the UK skills base in complementary model-based approaches to AI, which are needed for the development of safe and trusted AI systems. The scientists and engineers trained by the CDT will be experts in a range of model-based AI techniques, the synergies between them, their use in ensuring safe and trusted AI, and their integration with data-driven approaches. Importantly, because AI is increasingly pervasive in all spheres of human activity, and may increasingly be tied to regulation and legislation, the next generation of AI researchers must not only be experts on core AI technologies, but must also be able to consider the wider implications of AI on society, its impact on industry, and the relevance of safe and trusted AI to legislation and regulation. Core technical training will be complemented with skills and knowledge needed to appreciate the implications of AI (including Social Science, Law and Philosophy) and to expose them to diverse application domains (such as Telecommunications and Security). Students will be trained in responsible research and innovation methods, and will engage with the public throughout their training, to help ensure the societal relevance of their research. Entrepreneurship training will help them to maximise the impact of their work and the CDT will work with a range of industrial partners, from both the private and public sectors, to ensure relevance with industry and application domains and to expose our students to multiple perspectives, techniques, applications and challenges. This CDT is ideally equipped to deliver this vision. King's and Imperial are each renowned for their expertise in model-driven AI and provide one of the largest groupings of model-based AI researchers in the UK, with some of the world's leaders in this area. This is complemented with expertise in technical-related areas and in the applications and implications of AI.

Lancaster University (LU) proposes a Centre for Doctoral Training (CDT) to develop international research leaders in statistics and operational research (STOR) through a programme in which cutting-edge industrial challenge is the catalyst for methodological advance. Our proposal addresses the priority area 'Statistics for the 21st Century' through research training in cutting-edge modelling and inference for large, complex and novel data structures. It crucially recognises that many contemporary challenges in statistics, including those arising from industry, also engage with constraint, optimisation and decision. The proposal brings together LU's academic strength in STOR (>50FTE) with a distinguished array of highly committed industrial and international academic partners. Our shared vision is a CDT that produces graduates capable of the highest quality research with impact and equipped with an array of leadership and other skills needed for rapid career progression in academia or industry. The proposal builds on the strengths of an existing EPSRC-funded CDT that has helped change the culture in doctoral training in STOR through an unprecedented level of engagement with industry. The proposal takes the scale and scientific ambition of the Centre to a new level by: * Recruiting and training 70 students, across 5 cohorts, within a programme drawing on industrial challenge as the catalyst for research of the highest quality; * Ensuring all students undertake research in partnership with industry: 80% will work on doctoral projects jointly supervised and co-funded by industry; all others will undertake industrial research internships; * Promoting a culture of reproducible research under the mentorship and guidance of a dedicated Research Software Engineer (industry funded); * Developing cross-cohort research-clusters to support collaboration on ambitious challenges related to major research programmes; * Enabling students to participate in flagship research activities at LU and our international academic partners. The substantial growth in data-driven business and industrial decision-making in recent years has signalled a step change in the demand for doctoral-level STOR expertise and has opened the skills gap further. The current CDT has shown that a cohort-based, industrially engaged programme attracts a diverse range of the very ablest mathematically trained students. Without STOR-i, many of these students would not have considered doctoral study in STOR. We believe that the new CDT will continue to play a pivotal role in meeting the skills gap. Our training programme is designed to do more than solve a numbers problem. There is an issue of quality as much as there is one of quantity. Our goal is to develop research leaders who can innovate responsibly and secure impact for their work across academic, scientific and industrial boundaries; who can work alongside others with different skills-sets and communicate effectively. An integral component of this is our championing of ED&I. Our external partners are strongly motivated to join us in achieving these outcomes through STOR-i's cohort-based programme. We have little doubt that our graduates will be in great demand across a wide range of sectors, both industrial and academic. Industry will play a key role in the CDT. Our partners are helping to co-design the programme and will (i) co-fund and co-supervise doctoral projects, (ii) lead a programme of industrial problem-solving days and (iii) play a major role in leadership development and a range of bespoke training. The CDT benefits from the substantial support of 10 new partners (including Morgan Stanley, ONS Data Science Campus, Rolls Royce, Royal Mail, Tesco) and continued support from 5 existing partners (including ATASS, BT, NAG, Shell), with many others expected to contribute.