Exascale computing offers the prospect of running numerical models, for example of nuclear fusion and the climate, at unprecedented resolution and fidelity, but such models are still subject to uncertainty and we need to able to quantify such uncertainties (and for example use data on model outputs to calibrate the model inputs). Exascale computing comes at a cost. We will never be able to run huge ensembles go models on Exascale computers. Naive methods, such as Monte Carlo where we simply sample from the probability distribution of the model inputs, run a huge ensemble of models and produce a sample from the output distribution, are not going to be feasible. We need to develop uncertainty quantification methodology that allows us to efficiently, and effectively, perform sensitivity and uncertainty calculations with the minimum number of exascale model runs. Our methods are based on the idea of an emulator. An emulator is a statistical approximation linking model inputs and outputs in a fast non-linear way. It also includes a measure of its own uncertainty so we know how well it is approximating the original numerical model. Our emulators are based on Gaussian processes. Normally we would run a designed experiment and use these results to train the emulator. Because of the cost of exascale computing we use a hierarchy of models from fast, low fidelity versions through higher fidelity more computationally expensive ones to the very expensive, very high fidelity one at the apex of the hierarchy. Building a joint emulator for all the models in the hierarchy allows us to gain strength from the low fidelity ones to emulate the exascale models. Although such ideas have been around for a number of years they have not been exploited much for very large models. We will expand on the existing theory on a number of new ways. First we will look at the problem of design. To exploit the hierarchy to its fullest extent we need an experimental design that allocates model runs to the correct layer of the model hierarchy. We will extend existing sequential design methodology to work with hierarchies of model, not only finding the optimal next set of inputs for running the model but also which level it should be run in. We will also ensure that the sequential design is 'batch' sequential, allowing us to run ensembles rather than waiting for each run to return answers. Because the inputs and outputs of exascale models are often fields of correlated values we will develop methods for handling such high dimensional inputs and outputs and how to relate them to other levels of the hierarchy. Finally we will investigate whether AI methods other than Gaussian processes can be used to build efficient emulators.

Brazing is an important process for joining materials. It is quick and permits high strength, and is unique among high-temperature permanent joining methods in leaving the materials being joined largely unchanged; hence it can make complex joints and join dissimilar and difficult to weld materials (e.g. metals to ceramics and high Al/Ti content nickel superalloys respectively). It works by having a specific alloy, called a Brazing Filler Metal (BFM), introduced between the parts to be joined. Thermal treatment of the assembly is used to melt and solidify the BFM, forming a bond. These BFMs are designed specifically for different types of bonding situation, and can have many different compositions. Brazing is a key technology for many advanced applications, including the aerospace and nuclear sectors, but it has limitations. As the service requirements become more demanding, and base metals are refined, new BFMs must be developed. Some specific problems facing brazing technology today include: 1) Widening the spectrum of materials that can be joined (including higher temperature materials, bonding metals to ceramics, and also lower process temperatures for materials that cannot survive those of existing brazing alloys; functional ceramics and high strength 7000 series aluminium alloys, for example), would open up a whole host of novel technologies, using both existing and advanced materials in new ways 2) High temperature brazing uses additions such as boron or silicon to suppress the BFM melting point. They do this well, but also introduce brittle intermetallic phases in the joint region, limiting mechanical performance. 3) In practice, the parameters for brazing are determined on an application-specific basis, by experimental trial and error. Greater fundamental understanding of the brazing process will render this more efficient, permitting the brazing conditions to be designed. This project builds the understanding to address such challenges. A new type of alloy, High Entropy Alloys (HEAs) has recently come to the fore for alloy design. In these alloys, similar amounts of many elements are combined, rather than the typical approach of main solvent element with small additions of other elements to adjust the properties. Some HEAs have reported properties desirable for BFMs; e.g. the ability to add large amounts of elements to control melting point or wetting and flow behaviour without inducing brittle phases, and the multicomponent nature could mediate the transition in a joint between dissimilar materials. However, the physical metallurgy of HEAs is still relatively poorly understood, and their use in brazing has only been explored to a very limited extent. In this work we are investigating systematically the design, understanding and use of HEAs as BFMs. This both adds to our fundamental understanding of this intriguing new class of alloys, and provides the knowledge and skills to permit the design of new products for industry. The data and computer models of the brazing process we will generate give the design methods and data for the development of brazing parameters, which is currently done on a case-by-case basis. The project brings together the UK academic and industrial community on brazing for the first time, and will act as a focus for brazing interest. Aided by our industrial partners we will demonstrate the outcome of this work by two example case studies of alloy development: I) Reduced cost BFM for aero engines; current alloys contain significant amounts of Au and so a noble metal-free BFM, with appropriate performance, would reduce costs. II) Fusion BFM; to build advanced fusion reactor designs, it is necessary to join tungsten blocks on the reactor interior to copper pipes for coolant. This is currently done with BFMs with melting points <325degC; this limits operating temperatures. A new BFM would improve the performance and give more design flexibility for fusion reactor components.

Fusion reactors could some day provide a clean and nearly inexhaustible source of energy, but their development has proven to be challenging. Nevertheless, great progress has been made in recent decades and fusion research is now at a critical stage: ITER, the first test reactor anticipated to generate a surplus of energy, is being built and operation is planned to start around 2025. It will serve as a testbed for DEMO, a prototype for a commercially viable fusion power plant to be completed by 2050. The Culham Centre for Fusion Energy (CCFE) is a key contributor to this development: it operates the Joint European Torus (JET) which is currently the world's largest fusion test reactor. JET is important for experimental results and validation of simulation software, both of which are used to inform the design of the much larger ITER Computer simulations complementing experiments with test reactors are critical for the design and operation of ITER but also to explore alternative reactor designs. The immense complexity of the physics involved translates into complex mathematical models which take a long time to solve numerically, even on modern computer architectures. As reactors grow in size and complexity, so do the employed models and therefore solution times. LOCUST, for example, is a state-of-the-art particle tracker used operationally at CCFE and optimised heavily to exploit graphical processing unit (GPU) accelerators. However, one simulation of the trajectories of fast ions generated from neutral beam injection in the JET test reactor still takes around 10 hours to complete. Because of the higher energies, a similar simulation for ITER already takes 4 to 7 days. Therefore, at the moment, design choices can be informed only by a small number of simulations with carefully selected parameters. However, systematic exploration of a wide range of design parameters in computer simulations is not yet possible. The project will develop a new and more efficient algorithm and deploy it as a particle tracker in CCFE's operational simulation software. This will help to significantly reduce solution times and contribute toward the order of magnitude reduction of runtimes needed for effective in-silico design of components for ITER. While the new algorithm will be deployed for a specific application, the mathematical ideas developed during the project can help to improve the efficiency of computer simulations in other applications such as manufacturing processes involving plasmas, for example for flat panel displays or solar panels.

Summary For a lot of academic and industrial research into nuclear energy, using NNUF and other facilities, it is important that neutron-irradiated material of known provenance is available. Getting samples irradiated in reactors is both time-consuming and expensive, and as much use as possible should be made of existing material. There is a wide range of surveillance and other samples in the UK, owned by organisations like the Nuclear Decommissioning Authority (NDA), EDF Energy and Rolls-Royce. Establishing either a central or distributed archive of a selection of this material that can be accessed by researchers has been identified as a priority by the UK Government's Nuclear Innovation and Research Advisory Board (NIRAB). The archive is the second item in the table of favoured investments in EPSRC's NNUF Phase 2 call. While the Irradiated Materials Archive Group (IMAG), comprising universities, National Nuclear Laboratory (NNL), UK Atomic Energy Authority (UKAEA), NDA and other stakeholders, has developed this concept, further work is required before the key stakeholders are in a position to decide if and how to proceed. Options could range from leaving the material where it presently is and having systems that enable individuals to ascertain the material and pedigree available, and request samples for their research, to bringing samples from locations in the UK to dedicated stores at Sellafield (higher activities) and UKAEA's Culham site (low-activity). It is, therefore, proposed that the archive is taken forward in two stages. Stage 1 is an option study and the subject of this proposal. At the end of Stage 1, key stakeholders - including EPSRC, the owners of the material and the managers of proposed stores - would decide whether to proceed and with which option. Stage 2 would require a new proposal for funding based on cost estimates established in Stage 1. However, an upper bound for the latter is indicated in this proposal. Important considerations in Stage 1 include: ascertaining what material samples are available and which are of interest to UK researchers; logistical issues including ownership and liability, transport and waste disposal; and the requirements for the archive database(s). An attractive option for the last of these may be for NDA and other owners of material to manage their own databases in a way that permits users to interrogate these and request samples. UKAEA, NNL and the University of Bristol (UoB) propose to undertake Stage 1 and produce an options appraisal for EPSRC and its NNUF Management Team, having consulted all stakeholders. This would take 19 months and require £524,000. Wide-ranging support for this proposal is confirmed by letters from Dame Sue Ion (first chair of NIRAB), the CEO of the Henry Royce Institute for Advanced Materials and AWE. The NDA has been consulted in the drafting of this proposal and expressed its willingness to collaborate in the project, as has Rolls-Royce in its letter of support. The US has had a national archive for some years and learning from its experience would be part of this project; a letter confirming the value of the archive is from the Director of Nuclear Science User Facilities at Idaho National Laboratory.

This is currently one of the most exciting and dynamic periods for UK nuclear science & engineering since the 1950s. Inter alia, both new reactor build (essential to meet climate change targets) and the decommissioning of the UK's legacy nuclear sites (a 120 year, £121 bn programme) are driving forward, BEIS are investing heavily in the new national nuclear innovation programme and the sector deal for the industry has just been published. The already acute need for skilled nuclear scientists and engineers is therefore increasing and will continue to do so into the long term. To address these needs we propose a CDT in Nuclear Energy (GREEN), a partnership between 5 of the UK's leading nuclear universities and 12 industry partners, addressing EPSRC priority area 19: Nuclear Fission & Fusion for Energy. Evolving from the very successful Next Generation Nuclear (NGN) CDT, GREEN will deliver comprehensive doctoral training across the whole fission fuel cycle as well as in allied areas of fusion. Inspired by changes in external drivers and feedback from alumni, employers and funders, GREEN will offer both academically- and industrially- based research pathways, linked to enhanced employability training. We will further widen our already strong industry engagement by inclusion of new external partners, and align closely with other national and international activities, including other proposed CDTs. Experience from NGN suggests we will be able to leverage EPSRC support to give a typical cohort size of 15-20 students. Remarkably, using the leverage of 40 studentships from EPSRC, GREEN has already secured a further 47 studentships from Industry and Academia, ensuring a minimum number of 87 students in the GREEN CDT.