Addressing the broadest and most pressing issues facing the natural world requires a holistic understanding of the complex interactions that govern it. This requires the use of models - mathematical descriptions of the world - to explain observed trends, answer "what if?" questions and predict future trajectories. As these models evolve to match our increasing understanding of the natural world, so must the research software infrastructure that underpins them. Amongst other things, this software infrastructure is responsible for helping us link models together to assess the bigger picture, promoting trust in scientific results by making model results reproducible, letting us easily use models on the latest high-performance computers, providing a consistent computational environment and access to data to help developers collaborate, and providing interactive visualisations and apps of model results to a broader audience. To use an analogy - just as analytical scientists require access to laboratories full of high-tech equipment to perform scientific experiments, computational scientists require access to virtual laboratories full of the latest software infrastructure to perform computational experiments. Software infrastructure and communities have developed to begin to meet these challenges across the globe, and partners in this project have been leading these developments for several decades. However, these software and communities are currently independent and constrained, either by geography or to particular scientific domains. The goal of this project is to unite this infrastructure around an international community of practice, providing much needed international cohesion across environment modelling software infrastructure. United, this software has the potential to be truly transformative, enabling collaborative innovation where, for example: models can be readily deployed to and dynamically linked within the cloud; physics-based, statistical and data science models can work seamlessly together to provide a step change in how realistically our models predict the natural world, and; results can be shared easily to non-developers via interactive apps. We will showcase this transformative potential through a case study, which will predict the transport of microplastics in the environment from their release, through waterways and the terrestrial environment, out to the ocean. Plastic pollution is widespread and global, with plastic debris present in all parts of the environment, from deep ocean trenches to remote mountains. It poses a potentially significant risk to both the environment and ourselves. Despite this, the modelling of microplastic transport in the environment is in its infancy, and whilst models of individual compartments (rivers, oceans) exist, there are no frameworks capable of predicting high-resolution microplastic transport from source to sea. Our case study will solve this, at the same time as demonstrating the benefits yielded by our united software infrastructure. This infrastructure will underpin the case study, providing the tools needed to link together the hydrological, microplastic transport and coastal ocean models of which it comprises, and providing a collaborative virtual environment to power it. The result will be a modelling framework that not only offers a step change in our ability to predict microplastic transport from source to sea, but that is flexible enough to be adapted to different chemical classes, thereby making a significant contribution to our efforts towards a zero pollution society. We are a new partnership who collectively unites world-leading expertise in software infrastructure development, community building, hydrology, chemical fate modelling and oceanography. All partners are committed to securing a long-term, self-sustaining collaboration that will ultimately help advance environmental modelling far beyond the scope of this project.

Since the advent of numerical weather prediction in the early twentieth century, physics driven computational modelling has gone from strength to strength, underpinning much of the modern world, from the design of new bridges and buildings that can withstand earthquakes, to the aerodynamic optimisation of airplanes and the simulation of materials for batteries underpinning the electric car revolution. But physics based models alone have limits in what they can do. From high dimensional control problems to multiscale fluid flow, there are many important systems where conventional discretise-and-solve approaches remain permanently out reach. In other important systems, we have no physical models at all (in natural language processing and many other areas). In these data based approaches we have seen tremendous advances over the last decade, exemplified by the deep learning revolution. There is a now a growing consensus that computational models of tomorrow will consist of combinations of physics and data driven approaches and should not be viewed separately from each other. There is one more missing ingredient, attaining increasing recognition by research labs across the world, namely research software engineering. Traditionally seen as a professional service to support the implementation of computational models, research software engineering now emerges as an equal academic pillar to computational mathematics and data driven approaches. Software design, and hardware limitations, inform and shape the design of computational methods. Researchers need to take a holistic view across computational modelling and software engineering to create truly innovative solutions to the truly challenging problems from digital twins in personal medicine to simulating and mitigating the effects of climate change. This CDT has been designed around the need to train graduates across the interfaces of physics and data driven computational modelling and research software engineering. Our trainees will be able to engage with challenging problems not only from a modelling perspective but also from a software perspective, moving fluently across modelling and research software engineering. The subsequent urgent need for training in research software engineering at the highest level is also increasingly recognised by research centres across the world. We have partnered with a number of institutions in this proposal who follow this vision. In the UK this has been recently exemplified by the Independent Review of the Future of Compute, which recognised the importance of pairing infrastructure investments with skills programmes, and the importance of creating, attracting and retaining world class compute talent. Paired with an innovative training programme around interface working groups and software projects, our graduates will participate in and shape world leading research across the mathematics of data enhanced computational modelling, the design of corresponding computational algorithms, scientific research software engineering, and domain specific applications.

Software is fundamental to research, fulfilling many different roles - instrument, model, tool, infrastructure - across all disciplines. Recent shifts in the wider research landscape, e.g. inclusion of research software in policies developed by the OECD and UNESCO, necessitate new approaches to software sustainability and consolidation and scaling of existing initiatives to support research software (the software used in research) and digital research infrastructure (the compute, data, networking, software and people infrastructure) that enables it. Thus far, support for research software has tended to focus on individuals or national policies and standards. Moving forward, organisations such as universities and other research institutions will play an increasingly important role in ensuring research software culture and practice is adopted by the research community. This is essential to empower those engaged in research to fully harness the potential of software and foster the execution of excellent research. The Software Sustainability Institute (SSI) was established in 2010 as the first organisation in the world dedicated to the development and support of research software best practices. In its first phase (2010 - 2015), the SSI gained an understanding of the state of the nation of research software, its developers/users, its requirements, and the importance of software for conducting research. The second phase (2015 - 2019) focussed on supporting communities to become self-sustaining and campaigning for change in research culture. In the third phase (2018 - 2024), the SSI consolidated its position as world-leading experts in research software policy and best practices. The SSI also scaled up its highly successful activities to make them more sustainable in the longer term. Throughout, the SSI has fostered a large, collaborative, worldwide community of advocates and practitioners to help deliver on their motto: better software, better research. The fourth phase of the SSI will continue enhancing and scaling its signature activities, including the fellowship programme, community building, career development and training. It will continue to campaign for the recognition of all of the people and outputs that contribute to research and add a new focus on environmental sustainability and empowering organisations to take responsibility for the research software they create and use. Four impacts will guide the work in SSI-4: 1. Evidence-driven research software policy and guidance. 2. Capable research communities. 3. Widespread adoption of research software best practice. 4. Broadened access and contributions to the research software community. The SSI will achieve these through: - Building on its successful platforms and campaigns: empowering individuals through the Fellowship Programme, amplifying dissemination through online resources and social media, raising awareness of research software through events, and campaigning for policy and research culture change. - Growing its policy and research activities: building on SSI national landscape studies, collaborating on the HiddenREF campaign, creating new connections to further embed software into UK research policy. - Developing new training courses, learning pathways, communities of practice handbooks, and bringing the community together through the Collaborations Workshop. - Co-producing research to explore the barriers and enablers to career progress, commissioning articles and guides from a diverse range of authors, and running workshops in other, non-English, languages. - Coordinating an innovative software funding pilot to better understand how research software maintenance and development should be funded.

In Phases 1 (Prepare) and 2 (Deploy) we developed an understanding of the state of the nation of research software, its developers/users, its requirements, and how software is changing the way research is conducted. Building on our experience and expert understanding, Phase 3 (Expand) will focus on the creation of sustainable and self-supporting communities of practice to empower cultural change that enables better practice to be widely adopted to: foster a culture of sharing expertise and enabling; integrate project consultancy, training and awareness raising to effect and support change; move from local and individual actions to national and community level effects. Our goal is that the UK research community be enabled to take full advantage of software and, in doing so, to support the conduct of excellent research. Our objectives are: A) Widespread adoption of research best practice: agreeing and defining best practice with reference to research software, and enabling its widespread adoption to ensure the reliability and reproducibility of modern research. Enabling development of models and blueprints for initiating, nurturing and maturing communities of practice, enhancing our status in the UK and internationally as the go-to institution for insight into research software matters and catalysing new international collaborations. B) Cutting-edge policy and guidance: collaborating with stakeholders to create and disseminate evidence-based guidance, infrastructure, policies and tools. This leads to improved reusability of research software and its associated research outputs. C) A capable research community: based on a sustainable and scalable community-led model that will push the boundaries of knowledge across domains to maintain excellence and drive innovation and career paths, to increase the recognition of research software. Supporting collaboration in the UK research society and helping it become more resilient and sustainable will achieve an increased social and cultural impact. D) An open evidence bank: identifying and generating datasets, conducting analysis to provide insight and evidence of the importance of software, people and practices. This enables costing of resources required to develop, maintain and preserve research software. To achieve these goals, we will be: 1) Raising awareness: empower and develop a cohort of ambassadors for good practice through our Fellowship; outreach to stakeholders at all levels on research software issues; to deliver adoption of best practice. 2) Seeding change: build multiple sustainable Communities of Practice (CoP): for research domains, for techniques, for stakeholder groups, for UK institutions; set up expert panels that commission topic-based programmes of workshops, policy studies and outreach; nurture and scale existing CoPs e.g. through RSE exchanges; develop tools and services to support CoPs; to guarantee the widespread adoption of research best practice. 3) Providing expertise: create regional training hubs to continue growth of provision; commission new courses; refocus open call consultancy; conduct feasibility study for an RSE brokerage; to form a capable research community. 4) Influencing policy: publish new guidance and standards; work with international collaborators to put policy into practice; conduct research that improves understanding of research software; to deliver cutting-edge policy and guidance and build an open evidence bank.