The transport and mixing of constituents in fluid flows is of central importance to many areas of sciences and engineering. Numerous industrial processes, for instance, involve the mixing and in many cases reactions of chemicals dissolved in fluids. Transport and mixing are also crucial to several environmental issues, such as the dispersion of pollutants and the distribution of atmospheric greenhouse gases. Often, the constituents do not affect the fluid flow: they are then regarded as passive scalars, which are transported (advected) by a given flow, mixed by molecular diffusion, and possibly react chemically. The evolution of their concentration is governed by the advection-diffusion-reaction equation. If the flow is known, this equation predicts how the scalar concentration varies in time and space. However, in many applications, the flows are chaotic and too complex to be known exactly. In this case, a probabilistic approach is needed which relates the statistics of the scalar concentration to the statistics of the fluid flows, modelled by random processes. This project will develop such an approach. Its main aim is to devise mathematical tools that make it possible to describe the range of scalar evolutions that can be expected from an ensemble of possible flows rather than the response to a single flow. Its novelty is to go beyond the standard description in terms of ensemble averages in order to fully characterise the variability of the concentration between different flow realisations. The outcomes of the project will be (i) new mathematical results that relate this variability to flow characteristics such as stretching properties, and (ii) new numerical methods, based on ensemble simulations, that sample the variability at minimal computational cost. Particular attention will be paid to rare events which lead to extreme values of the concentration. For example, when a scalar is released in a random flow, there is a small probability that it disperses only weakly and hence that its concentration remains high for a long time. Probabilities of this type have a clear practical importance, for instance for the assessment of the risk posed by pollution sources; their reliable estimation is one of the challenges addressed by the project. Three applications, all of them with environmental significance, have been chosen to serve as testbeds for the new developments. These involve: (i) water vapour, which condenses in low-temperature regions, (ii) ozone, which is depleted by its reaction with active chlorine, and (ii) phytoplankton, which experiences a logistic evolution while being advected. These applications are representative of a much broader class of problems, characterised by weak diffusion and well-mixed initial conditions, to which the methods devised can be applied. Beyond this, the results will be relevant to a number of other systems modelled by infinite-dimensional random dynamical systems.

Imagine a world in which every individual can be routinely and extensively health monitored, in a time-efficient and safe manner, without having to visit an oversubscribed, centralised medical centre with limited access and appointment flexibility. Imagine a new clinical paradigm where early diagnosis becomes the standard, even in remote areas, within low-income demographics and for international travel, due to ubiquitous, modular, high-resolution X-ray imaging systems with automated diagnosis and live reporting; where frequent imaging contributes to a large diagnostic portfolio of individuals over time (whilst maintaining privacy) and advanced artificial-intelligence (AI)-based algorithms use these anonymous data sets acquired across the population to identify extremely early stages of disease - transforming preventative medicine as we know it. This is the 2050 that ReImagine will enable. We will revolutionise the use of X-rays for medical imaging through low-dose, high-resolution and inexpensive computed tomography (CT) scanners, where highly innovative hardware and software components will be developed side-by-side to enable automated all-in-one pre-symptomatic diagnosis. Our vision will be enabled by developing highly sensitive X-ray detectors using scalable halide perovskite (PVK) semiconductors - materials currently making impact as disruptive photovoltaic (PV) technologies - for phase contrast X-ray imaging, in conjunction with AI-driven algorithms for image reconstruction, lesion detection and segmentation. This will realise quicker and more efficient healthcare delivery and prevent disease spread through extremely early detection of disease (e.g., those otherwise responsible for future pandemics) and for routine follow-up of oncology patients (e.g. early detection of cancer recurrence). To realise this extremely challenging vision - combining breakthroughs in hardware, software and end-user application - we have uniquely assembled a world-leading, cross-cutting team from the Universities of Cambridge, Loughborough and Leicester, together with academic partners at the University of Leiden and industry partners in GE Healthcare, Scintacor, Cheyney and Immaterials Labs, bringing combined expertise spanning materials synthesis and scaling, characterisation and modelling, device assembly, detector physics, mathematics, CT systems development, and clinical radiology. The hardware will be interweaved with the software and algorithm development, with both guided by clinical insight, industry and case studies to ensure fit for end users.

Uncertainty quantification, verification and validation are crucial to establish the reliability and reproducibility of all forms of computer-based simulation. We propose to establish an open source and open development VVUQ toolkit optimised for efficient execution at current pre- and emerging exascale, which will raise new challenges and new opportunities for simulations in fields as diverse as fusion and climate modelling. Computer simulation results are validated compared with experiment in several ways, ranging from qualitative to quantitative measures which apply a validation metric. Likewise, verification is concerned with confirmation that the mathematical model and corresponding algorithm have been coded correctly. Uncertainty quantification (UQ) is concerned with understanding the origins of and assessing the magnitudes of the errors which accompany computer simulations, whether epistemic or aleatoric. VVUQ is necessary for any simulation that makes predictions in advance of an event to become actionable - that is, for its output to be useful in any form of decision-making process, from government interventions in pandemics to the choice of materials to combine for aircraft wing production. Here, exascale computing offers more opportunities to make actionable predictions. Moreover, because VVUQ is intrinsically compute intensive due to its ensemble-based execution pattern, it too requires exascale resources, as well as advanced resource management strategies to efficiently manage the large numbers of concurrent runs necessary. We propose to establish an open source and open development VVUQ toolkit optimised for efficient execution at current pre- and emerging exascale. This will include advanced approaches for surrogate modelling in order to minimise the expense and time needed to perform the most compute-intensive calculations and will demonstrate its efficiency gains for a diverse array of VVUQ workflows within multiple scientific applications, and on architecturally and geographically diverse emerging exascale environments. The software developed, implemented and benchmarked in this project will become an open and invaluable asset to the UK ExCALIBUR community but also much more widely within UK and internationally as high-performance computing enters the exascale era. The proposed exascale toolkit will be built on a combination of widely used tools and services which will be evolved to handle systems of increasing levels of complexity. These include components from the VECMA project (EasyVVUQ, FabSim3, QCG-PJ and EasySurrogate), as well as the UCL-Alan Turing Institute Multi-Output Gaussian Process Emulator (MOGP). We will apply these capabilities to several applications, including: (i) the UKAEA's tokamak fusion modelling use case for which a working software environment will be produced; (ii) weather and climate forecasting for the Met Office; (iii) turbulent flow simulation for environmental science; (iv) prediction of advanced materials properties of graphene-polymer based nanocomposites for aerospace applications; (v) high-fidelity patient-specific virtual human blood flow system for medical research; (vi) drug discovery; and (vii) human migration.

Overview: We propose a Centre for Doctoral Training in Data Science. Data science is an emerging discipline that combines machine learning, databases, and other research areas in order to generate new knowledge from complex data. Interest in data science is exploding in industry and the public sector, both in the UK and internationally. Students from the Centre will be well prepared to work on tough problems involving large-scale unstructured and semistructured data, which are increasingly arising across a wide variety of application areas. Skills need: There is a significant industrial need for students who are well trained in data science. Skilled data scientists are in high demand. A report by McKinsey Global Institute cites a shortage of up to 190,000 qualified data scientists in the US; the situation in the UK is likely to be similar. A 2012 report in the Harvard Business Review concludes: "Indeed the shortage of data scientists is becoming a serious constraint in some sectors." A report on the Nature web site cited an astonishing 15,000% increase in job postings for data scientists in a single year, from 2011 to 2012. Many of our industrial partners (see letters of support) have expressed a pressing need to hire in data science. Training approach: We will train students using a rigorous and innovative four-year programme that is designed not only to train students in performing cutting-edge research but also to foster interdisciplinary interactions between students and to build students' practical expertise by interacting with a wide consortium of partners. The first year of the programme combines taught coursework and a sequence of small research projects. Taught coursework will include courses in machine learning, databases, and other research areas. Years 2-4 of the programme will consist primarily of an intensive PhD-level research project. The programme will provide students with breadth throughout the interdisciplinary scope of data science, depth in a specialist area, training in leadership and communication skills, and appreciation for practical issues in applied data science. All students will receive individual supervision from at least two members of Centre staff. The training programme will be especially characterized by opportunities for combining theory and practice, and for student-led and peer-to-peer learning.