Composite materials and advanced structures are predicted to be major drivers for the growth and competitiveness of UK's value-added manufacturing economy. Maintaining and further enhancing the current national competitive advantage has been identified as a government strategic priority. This fellowship will contribute toward this goal by considering engineering structural design and composite materials in a different light. When conceiving structures, it is common practice to rely on well-established design principles and robust analysis tools. This may be for several reasons, but the lack of experience with different approaches is probably the most important. Exploring the opportunities that are available outside the 'designer comfort zone' is a risky, expensive and time-consuming gamble that engineering companies can rarely afford to take. History shows several examples of structural designs that, despite being at the forefront of current material technologies, missed out on remarkable engineering opportunities. The Iron Bridge, across the river Severn near Coalbrookdale, is probably the most famous case in point in Britain. Completed in 1779, the bridge was the world's first to be made of cast iron and is renowned for being substantially overdesigned, having been conceived following rules for wood rather than metal constructions. Composite materials are a modern example. One of their most remarkable features is the versatility that allows engineers to design not only a structure but also its constituent materials. However, partly due to their excellent specific stiffness, there is often the tendency to use them to replicate the well-known behaviour of isotropic materials, thus missing the opportunity to exploit many of the benefits that they could potentially provide. Owing to the colour of carbon fibre composites, this modus operandi is known as the 'black metal' approach. In a similar way, structural design is normally limited to linear regimes. In other words, structures are often designed to be stiff and exhibit small displacements, i.e. to respond linearly to the applied loads. Under these circumstances design methods are well established and based on decades of experience. This is indeed the engineer's comfort zone. Designers usually avoid large displacements because they may cause unwanted shape changes and trigger the transition to nonlinear regimes, potentially leading to catastrophic and often sudden, uncontrolled failure. However, if we could learn to control such behaviour, it could actually be exploited for a benefit. The aim of this proposal is to explore the possibilities given by nonlinear responses in structural design. The principal objectives are the development of a new generation of adaptive/multifunctional structures working in elastically nonlinear regimes and the creation of novel paradigms for structural efficiency. The ambition is to harness the possibilities presented by composite materials and to deliver new design principles by removing the barriers imposed by the current practice of restricting structures to behave linearly. Imagine aircraft wings or wind turbine blades tailored to be lighter and still meet the requirements imposed at different operating conditions, thanks to nonlinear stiffness characteristics; buildings whose structural response is compliant only if subjected to extreme earthquake loads, so as to prevent catastrophic failure; or a bridge whose stiffness increases in case of strong winds preventing detrimental aeroelastic instabilities. This is my vision. This is what the elastic properties of composite materials can offer, if we move away from the 'black metal' approach.

The aerospace industry is at a turning point: environmental concerns, legal frameworks and new energy sources mean that the industry needs to explore a different structural design space for composite aircraft configurations. Yet this is not readily possible using the slower experimentally-heavy design pyramid followed by industry in the past. The above scenario makes a compelling case for numerical structural design of very large integrated composite aircraft structures, but this problem is intractable. My vision is that structural design of very large composite structures can be enabled by a new simulation paradigm: I propose that, during the analysis, CAE models of very large structures adapt in real-time the scale of idealisation as required (adaptive multiscale), adapt in real-time the configuration of the structure (adaptive configuration), and where intelligent algorithms work at the back-end (HPC cluster) to extract high-value data from over 1 Tb output databases as they are being built. This paradigm will enable numerical design of very large integrated composite structures, thus having a significant impact on the emergence of much-needed new aircraft configurations.

Heart disease is the leading cause of disability and death in the UK and worldwide, resulting in enormous health care costs. Risk prediction on an individual patient basis is imperfect. Advanced medical development has already saved many lives, particularly in systolic heart failure. However, there is currently no treatment option for diastolic heart failure (with preserved ejection fraction) due to its complexity of multiple mechanisms and co-modality. Structural heart diseases, such as myocardial infarction (MI- commonly known as heart attack) and mitral regurgitation (MR, a leakage of blood through the mitral valve to left atrium in systole), where biomechanical factors are crucial, are often precursors to heart failure. MI can eventually lead to dilated heart failure despite immediate treatments post-MI. MR can induce pulmonary hypertension and oedema and subsequently, right heart overload and heart failure. The grand challenge is for these situations the heart simply cannot be modelled as an isolated left ventricle (as in most of the current studies); flow-structure interaction (FSI), heart-valve interaction, multiscale soft tissue mechanics, and tissue growth and remodelling (G&R) all play important roles in the progression of the structural diseases. This project is set up to meet this challenge by delivering a multiscale computational framework to include Whole-Heart FSI with G&R. Making use of the novel mathematical tools (constitutive laws, G&R, upscaling and statistical inference) developed by SofTMech, I will build a realistic four-chamber heart model that include heart-valve, chamber-chamber, heart-blood, and heart-circulation interactions, which will be powerful enough to model MI, MR and their pathological consequences. This work will be in close collaboration with my clinical, industrial and academic collaborators. The model will quantify which factors lead to adverse G&R and what variations are to be expected as the disease progresses. We will also identify significant biomechanical markers (e.g. constitutive parameters, energy indices, stress/strain evolution). The predictive values of these biomechanical parameters will be assessed against other established predictors of adverse remodellings, such as duration of ischaemia, final coronary flow grade after a primary percutaneous coronary intervention, and microvascular obstruction revealed by MRI. Thus, this project will generate new testable hypotheses and will be a significant step up towards more consistent decision-support for clinicians, since increasingly the pace and complexity of medical advances outstrip the ability of individual clinicians to cope with. Due to the statistical emulation and uncertainty quantification built into the project, the model predictions will be fast and quantified with error bounds on the outcome of alternative treatments. Consequently, we will also address the critical aspect of convincing clinicians that information obtained from simulations will be correct and relevant to their daily practice. The proposed research is right within the Healthcare Technologies "Optimising Treatment" and "Developing Future Therapies" priority areas, as well as targeting "New Connections from Mathematical Sciences", and "Statistics and Applied Probability" of Mathematical Sciences.

Machine learning (ML), in particular Deep Learning (DL) is one of the fastest growing areas of modern science and technology, which has potentially enormous and transformative impact on all areas of our life. The applications of DL embrace many disciplines such as (bio-)medical sciences, computer vision, the physical sciences, the social sciences, speech recognition, gaming, music and finance. DL based algorithms are now used to play chess and GO at the highest level, diagnose illness, drive cars, recruit staff and even make legal judgements. The possible applications in the future are almost unlimited. Perhaps DL methods will be used in the future to predict the weather and climate, of even human behaviour. However, alongside this explosive growth has been a concern that there is a lack of explainability behind DL and the way that DL based algorithms make their decisions. This leads to a lack of trustworthiness in the use of the algorithms. A reason for this is that the huge successes of deep learning is not well understood, the results are mysterious, and there is a lack of a clear link between the data training DL algorithms (which is often vague and unstructured) and the decisions made by these algorithms. Part of the reason for this is that DL has advanced so fast, that there is a lack of understanding of its foundations. According to the leading computer scientist Ali Rahimi at NIPS 2017: 'We say things like "machine learning is the new electricity". I'd like to offer another analogy. Machine learning has become alchemy!' Indeed, despite the roots of ML lying in mathematics, statistics and computer science there currently is hardly any rigorous mathematical theory for the setup, training and application performance of deep neural networks. We urgently need the opportunity to change machine learning from alchemy into science. This programme grant aims to rise to this challenge, and, by doing so, to unlock the future potential of artificial intelligence. It aims to put deep learning onto a firm mathematical basis, and will combine theory, modelling, data, computation to unlock the next generation of deep learning. The grant will comprise an interlocked set of work packages aimed to address both the theoretical development of DL (so that it becomes explainable) and the algorithmic development (so that it becomes trustworthy). These will then be linked to the development of DL in a number of key application areas including image processing, partial differential equations and environmental problems. For example we will explore the question of whether it is possible to use DL based algorithms to forecast the weather and climate faster and more accurately than the existing physics based algorithms. The investigators on the grant will be doing both theoretical investigations and will work with end-users of DL in many application areas. Mindful that policy makers are trying to address the many issues raised by DL, the investigators will also reach out to them through a series of workshops and conferences. The results of the work will also be presented to the public at science festivals and other open events.

In the diagnosis and treatment of disease, clinicians base their decisions on understanding of the many factors that contribute to medical conditions, together with the particular circumstances of each patient. This is a "modelling" process, in which the patient's data are matched with an existing conceptual framework to guide selection of a treatment strategy based on experience. Now, after a long gestation, the world of in silico medicine is bringing sophisticated mathematics and computer simulation to this fundamental aspect of healthcare, adding to - and perhaps ultimately replacing - less structured approaches to disease representation. The in silico specialisation is now maturing into a separate engineering discipline, and is establishing sophisticated mathematical frameworks, both to describe the structures and interactions of the human body itself, and to solve the complex equations that represent the evolution of any particular biological process. So far the discipline has established excellent applications, but it has been slower to succeed in the more complex area of soft tissue behaviour, particularly across wide ranges of length scales (subcellular to organ). This EPSRC SoftMech initiative proposes to accelerate the development of multiscale soft-tissue modelling by constructing a generic mathematical multiscale framework. This will be a truly innovative step, as it will provide a common language with which all relevant materials, interactions and evolutions can be portrayed, and it will be designed from a standardised viewpoint to integrate with the totality of the work of the in silico community as a whole. In particular, it will integrate with the EPSRC MultiSim multiscale musculoskeletal simulation framework being developed by SoftMech partner Insigneo, and it will be validated in the two highest-mortality clinical areas of cardiac disease and cancer. The mathematics we will develop will have a vocabulary that is both rich and extensible, meaning that we will equip it for the majority of the known representations required but design it with an open architecture allowing others to contribute additional formulations as the need arises. It will already include novel constructions developed during the SoftMech project itself, and we will provide many detailed examples of usage drawn from our twin validation domains. The project will be seriously collaborative as we establish a strong network of interested parties across the UK. The key elements of the planned scientific advances relate to the feedback loop of the structural adaptations that cells make in response to mechanical and chemical stimuli. A major challenge is the current lack of models that operate across multiple length scales, and it is here that we will focus our developmental activities. Over recent years we have developed mathematical descriptions of the relevant mechanical properties of soft tissues (arteries, myocardium, cancer cells), and we have access to new experimental and statistical techniques (such as atomic force microscopy, MRI, DT-MRI and model selection), meaning that the resulting tools will bring much-need facilities and will be applicable across problems, including wound healing and cancer cell proliferation. The many detailed outputs of the work include, most importantly, the new mathematical framework, which will immediately enable all researchers to participate in fresh modelling activities. Beyond this our new methods of representation will simplify and extend the range of targets that can be modelled and, significantly, we will be devoting major effort to developing complex usage examples across cancer and cardiac domains. The tools will be ready for incorporation in commercial products, and our industrial partners plan extensions to their current systems. The practical results of improved modelling will be a better understanding of how our bodies work, leading to new therapies for cancer and cardiac disease.