Computational science is a multidisciplinary research endeavour spanning applied mathematics, computer science and engineering together with input from application areas across science, technology and medicine. Advanced simulation methods have the potential to revolutionise not only scientific research but also to transform the industrial economy, offering companies a competitive advantage in their products, better productivity, and an environment for creative exploration and innovation. The huge range of topics that computational science encapsulates means that the field is vast and new methods are constantly being published. These methods relate not only to the core simulation techniques but also to problems which rely on simulation. These problems include quantifying uncertainty (i.e. asking for error bars), blending models with data to make better predictions, solving inverse problems (if the output is Y, what is the input X?), and optimising designs (e.g. finding a vehicle shape that is the most aerodynamic). Unfortunately, the process through which advanced new methods find their way into applications and industrial practice is very slow. One of the reasons for this is that applying mathematical algorithms to complex simulation models is very intrusive; mostly they cannot treat the simulation code as a "black box". They often require rewriting of the software, which is very time consuming and expensive. In our research we address this problem by using automating the generation of computer code for simulation. The key idea is that the simulation algorithm is described in some abstract way (which looks as much like the underlying mathematics as possible, after thinking carefully about what the key aspects are), and specialised software tools are used to automatically build the computer code. When some aspect of the implementation needs to change (for example a new type of computer is being used) then these tools can be used to rebuild the code from the abstract description. This flexibility dramatically accelerates the application of advanced algorithms to real-world problems. Consider the example of optimising the shape of a Formula 1 car to minimise its drag. The optimisation process is highly invasive: it must solve auxiliary problems to learn how to improve the design, and it be able to modify the shape used in the simulation at each iteration. Typically this invasiveness would require extensive modifications to the simulation software. But by storing a symbolic representation of the aerodynamic equations, all operations necessary for the optimisation can be generated in our system, without needing to rewrite or modify the aerodynamics code at all. The research goal of our platform is to investigate and promote this methodology, and to produce publicly available, sustainable open-source software that ensures its uptake. The platform will allow us to make advances in our software approach that enables us to continue to secure industrial and government funding in the broad range of application areas we work in, including aerospace and automotive sectors, renewable energy, medicine and surgery, the environment, and manufacturing.

Risk is the potential of experiencing a loss when a system does not operate as expected due to uncertainties. Its assessment requires the quantification of both the system failure potential and the multi-faceted failure consequences, which affect further systems. Modern industries (including the engineering and financial sectors) require increasingly large and complex models to quantify risks that are not confined to single disciplines but cross into possibly several other areas. Disasters such as hurricane Katrina, the Fukushima nuclear incident and the global financial crisis show how failures in technical and management systems cause consequences and further failures in technological, environmental, financial, and social systems, which are all inter-related. This requires a comprehensive multi-disciplinary understanding of all aspects of uncertainty and risk and measures for risk management, reduction, control and mitigation as well as skills in applying the necessary mathematical, modelling and computational tools for risk oriented decision-making. This complexity has to be considered in very early planning stages, for example, for the realisation of green energy or nuclear power concepts and systems, where benefits and risks have to be considered from various angles. The involved parties include engineering and energy companies, banks, insurance and re-insurance companies, state and local governments, environmental agencies, the society both locally and globally, construction companies, service and maintenance industries, emergency services, etc. The CDT is focussed on training a new generation of highly-skilled graduates in this particular area of engineering, mathematics and the environmental sciences based at the Liverpool Institute for Risk and Uncertainty. New challenges will be addressed using emerging probabilistic technologies together with generalised uncertainty models, simulation techniques, algorithms and large-scale computing power. Skills required will be centred in the application of mathematics in areas of engineering, economics, financial mathematics, and psychology/social science, to reflect the complexity and inter-relationship of real world systems. The CDT addresses these needs with multi-disciplinary training and skills development on a common mathematical platform with associated computational tools tailored to user requirements. The centre reflects this concept with three major components: (1) Development and enhancement of mathematical and computational skills; (2) Customisation and implementation of models, tools and techniques according to user requirements; and (3) Industrial and overseas university placements to ensure industrial and academic impact of the research. This will develop graduates with solid mathematical skills applied on a systems level, who can translate numerical results into languages of engineering and other disciplines to influence end-users including policy makers. Existing technologies for the quantification and management of uncertainties and risks have yet to achieve their significant potential benefit for industry. Industrial implementation is presently held back because of a lack of multidisciplinary training and application. The Centre addresses this problem directly to realise a significant step forward, producing a culture change in quantification and management of risk and uncertainty technically as well as educationally through the cohort approach to PGR training.