Optimisation -- the problem of identifying a satisficing solution among a vast set of candidates -- is not only a fundamental problem in Artificial Intelligence and Computer Science, but essential to the competitiveness of UK businesses. Real-world optimisation problems are often tackled using evolutionary algorithms, which are optimisation techniques inspired by Darwin's principles of natural selection. Optimisation with classical evolutionary algorithms has a fundamental problem. These algorithms depend on a user-provided fitness function to rank candidate solutions. However, for real world problems, the quality of candidate solutions often depend on complex adversarial effects such as competitors which are difficult for the user to foresee, and thus rarely reflected in the fitness function. Solutions obtained by an evolutionary algorithm using an idealised fitness function, will therefore not necessarily perform well when deployed in a complex and adversarial real-world setting. So-called co-evolutionary algorithms can potentially solve this problem. They simulate a competition between two populations, the "prey" which attempt to discover good solutions, and the "predators" which attempt to find flaws in these. This idea greatly circumvents the need for the user to provide a fitness function which foresees all ways solutions can fail. However, due to limited understanding of their working principles, co-evolutionary algorithms are plagued by a number of pathological behaviours, including loss of gradient, relative over-generalisation, and mediocre objective stasis. The causes and potential remedies for these pathological behaviours are poorly understood, currently limiting the usefulness of these algorithms. The project has been designed to bring a break-through in the theoretical understanding of co-evolutionary algorithms. We will develop the first mathematically rigorous theory which can predict when a co-evolutionary algorithm reaches a solution efficiently, and when pathological behaviour occurs. This theory has the potential to make co-evolutionary algorithms a reliable optimisation method for complex real-world problems.

The EPSRC Centre for Doctoral Training in Statistics and Machine Learning (StatML) will address the EPSRC research priority of the 'physical and mathematical sciences powerhouse' through an innovative cohort-based training program. StatML harnesses the combined strengths of Imperial and Oxford, two world-leading institutions in statistics and machine learning, in collaboration with a broad spectrum of industry partners, to nurture the next generation of leaders in this field. Our students will be at the forefront of advancing the core methodologies of data science and AI, crucial for unlocking the value inherent in data to benefit industry and society. They will be equipped with advanced research, technical, and practical skills, enabling them to make tangible real-world impacts. Our students will be ethical and responsible innovators, championing reproducible research and open science. Collaborating with students, charities and equality experts, StatML will also pioneer a comprehensive strategy to promote inclusivity, attract individuals from diverse backgrounds and eliminate biases. This will help diversify the UK's future statistics and machine learning workforce, essential for ensuring data science is used for public good. Data science and AI are now part of our everyday lives, transforming all sectors of the economy. To future-proof the UK's prosperity and security, it is essential to develop new methodology, specifically tailored to meet the big societal challenges of the future. The techniques underpinning such methods are founded in statistics and machine learning. Through close collaboration with a broad range of industry partners, our cohort-based training will support the UK in producing a critical mass of world-leading researchers with expertise in developing cutting-edge, impactful statistical and machine learning methodology and theory. It is well documented in government and learned society reports that the UK economy has an urgent need for these people. The significant level of industry support for our proposal also highlights the necessity of filling this gap in the UK data science ecosystem. StatML will learn from and build upon our previous successful experiences in cohort training of doctoral students (our existing StatML CDT funded in 2018, as well as other CDTs at Imperial and Oxford). Our students will continue to produce impactful, internationally leading research in statistics and machine learning (as evidenced by our students' impressive publication record and our world-leading research environment, as rated by the REF 2021 evaluation), while complementing this with a bespoke cohort-based Advanced Training program in Statistics and Machine Learning (StatML-AT). StatML-AT has been developed from our experience and in partnership with industry. It will be responsive to emerging technologies and equip our students with the practical skills required to transform how data is used. It will be delivered by our outstanding academics from both institutions alongside with industry leaders to ensure that students receive training in cutting edge technologies, along with the latest ideas in ethics, responsible innovation, sustainability and entrepreneurship. This will be complemented by industrial and academic placements to allow the students to develop their own international network and produce high-impact research. Together, StatML and its partners will train 90+ students over 5 cohorts. More than half of these will be funded from external sources, including 25+ by industry, representing excellent value for money. Our diverse cohorts will benefit from a unique and responsive training program combining academic excellence, industry engagement, and interdisciplinary culture. This will make StatML a vibrant research environment inspiring the next methodological advancements to transform the use of data and AI across industry and society.

Energy networks are vitally important enablers for the UK energy sector and therefore UK industry and society. The energy trilemma (energy security, environmental impact and social cost) presents many complex interconnected challenges which reach beyond the UK and have huge relevance internationally. These challenges vary considerably from region to region, and change as a result of technology and society changes. Therefore, the planning, design and operation of energy networks needs to be revisited and optimised. Current energy networks research does not fully embrace a whole systems approach and is therefore not developing a deep enough understanding of the interconnected and interdependent nature of energy network infrastructure. The Supergen Energy Networks Hub will provide leadership, a core research programme and mechanisms/funding for the energy networks community to grow and come together to develop this deeper understanding and explore opportunities to shape energy networks which are fit for the future. The research component of the Hub's activities comprises an interconnected and complementary series of work packages. The work packages are: WP1: Understanding, Shaping and Challenging; WP2: Energy Network Infrastructure; WP3: ICT and Data; WP4: Policy and Society; WP5: Markets and Regulation; WP6: Risk and Uncertainty. WP1 incorporates a co-evolutionary approach and brings the other work packages together in a structured way. WP2 is the backbone of the research, dealing with the physical infrastructure in a multi vector manner from the outset. WP3 to WP6 deal with aspects of energy networks that cut across, and are equally valid, for all vectors and have the ability to integrate and modernise network infrastructures. All work packages will consider both planning and design as well as operational aspects. Experimental work and demonstrators will be essential to progress in energy networks research and the Hub will bring these facilities to bear through WP1. The Hub will engage with the energy networks communities throughout the research programme, to ensure that the work is informed by best practice and that the findings are widely visible and understood. The main objectives of the communication and engagement activities will be to ensure the energy networks academic community are connected and coherent, and that their work has a high profile and deep level of understanding in the relevant Industrial, Governmental and Societal communities both nationally and internationally. This will maximise the chances of high impact outcomes in the energy networks space as well as promoting energy networks as an exciting and dynamic area to carry out research, thus attracting the brightest minds to get involved. Communication and engagement activities will be a constant feature of the Hub and will be particularly energetic during the first twelve months in order to rapidly establish a brand, and an open and supportive culture within the relevant communities. Engagement activities will as far as possible be carried out in conjunction with other key organisations in the energy space, to maximise the value of the engagement activities. The Hub aims to become a beacon for equality, diversity and inclusion. Our mission is to enhance equality of opportunity and create a positive, flourishing, safe and inclusive environment for everyone associated with the Hub, from staff, students, Advisory Board members and general Hub representation (at conferences, workshops and reviews). We recognise the need and the challenges to support early career researchers, and improve the balance of protected characteristics across the entire Hub community, such as race or ethnicity, gender reassignment, disability, sex, sexual orientation, age, religion or belief, pregnancy or maternity status, marital status or socio-economic background.

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.

Energy networks are vitally important enablers for the UK energy sector and therefore UK industry and society. The energy trilemma (energy security, environmental impact and social cost) presents many complex interconnected challenges which reach beyond the UK and have huge relevance internationally. These challenges vary considerably from region to region, and change as a result of technology and society changes. Therefore, the planning, design and operation of energy networks needs to be revisited and optimised. Current energy networks research does not fully embrace a whole systems approach and is therefore not developing a deep enough understanding of the interconnected and interdependent nature of energy network infrastructure. The Supergen Energy Networks Hub will provide leadership, a core research programme and mechanisms/funding for the energy networks community to grow and come together to develop this deeper understanding and explore opportunities to shape energy networks which are fit for the future. The research component of the Hub's activities comprises an interconnected and complementary series of work packages. The work packages are: WP1: Understanding, Shaping and Challenging; WP2: Energy Network Infrastructure; WP3: ICT and Data; WP4: Policy and Society; WP5: Markets and Regulation; WP6: Risk and Uncertainty. WP1 incorporates a co-evolutionary approach and brings the other work packages together in a structured way. WP2 is the backbone of the research, dealing with the physical infrastructure in a multi vector manner from the outset. WP3 to WP6 deal with aspects of energy networks that cut across, and are equally valid, for all vectors and have the ability to integrate and modernise network infrastructures. All work packages will consider both planning and design as well as operational aspects. Experimental work and demonstrators will be essential to progress in energy networks research and the Hub will bring these facilities to bear through WP1. The Hub will engage with the energy networks communities throughout the research programme, to ensure that the work is informed by best practice and that the findings are widely visible and understood. The main objectives of the communication and engagement activities will be to ensure the energy networks academic community are connected and coherent, and that their work has a high profile and deep level of understanding in the relevant Industrial, Governmental and Societal communities both nationally and internationally. This will maximise the chances of high impact outcomes in the energy networks space as well as promoting energy networks as an exciting and dynamic area to carry out research, thus attracting the brightest minds to get involved. Communication and engagement activities will be a constant feature of the Hub and will be particularly energetic during the first twelve months in order to rapidly establish a brand, and an open and supportive culture within the relevant communities. Engagement activities will as far as possible be carried out in conjunction with other key organisations in the energy space, to maximise the value of the engagement activities. The Hub aims to become a beacon for equality, diversity and inclusion. Our mission is to enhance equality of opportunity and create a positive, flourishing, safe and inclusive environment for everyone associated with the Hub, from staff, students, Advisory Board members and general Hub representation (at conferences, workshops and reviews). We recognise the need and the challenges to support early career researchers, and improve the balance of protected characteristics across the entire Hub community, such as race or ethnicity, gender reassignment, disability, sex, sexual orientation, age, religion or belief, pregnancy or maternity status, marital status or socio-economic background.