Simulations of cosmic structure formation address multi-scale, multi-physics problems of vast proportions. These calculations are presently at the forefront of today's use of supercomputers, and are important scientific drivers for the future use of exaflop computing platforms. However, continued future success in this field requires the development of new numerical methods that excel in accuracy, robustness, parallel scalability, and physical fidelity to the processes relevant in galaxy and star formation. In an interdisciplinary and international effort of astrophysicists and applied mathematicians we will in this project substantially improve the astrophysical moving-mesh code AREPO and extend its range of applicability, with the goal of producing an internationally leading application code for the upcoming large computing platforms. We work on new, powerful high-order discontinuous Galerkin schemes, on more efficient solvers for gravity and for anisotropic transport of heat and relativistic particles, and on an improvement of the accuracy of the treatment of ideal magnetohydrodynamics. We aim to drastically enhance the raw performance and scalability of the code by employing sophisticated hybrid parallelisation techniques combined with low-level optimizations that make full use of vector instructions and device accelerators. We will apply our code on current state-of-the art supercomputers to carry out transformative magnetohydrodynamic simulations of galaxy and primordial star formation, stretching the envelope of what is possible today and in the years to come. We will also work towards publicly releasing the AREPO and GADGET-4 codes.

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.