We live in the "Era of Mathematics" (UKRI, 2018), in which mathematics research has deep and widespread impact. Medical imaging is enhanced using the theory of inverse problems. Predicting sewage contamination in waterways after storms requires solving complicated systems of hydrodynamic equations. Machine learning tools are revolutionising data-intensive computing and, handled with proper mathematical care, have vast potential benefits for science and society. These are examples of the ongoing explosion in mathematical innovation driving, and being driven by, the analysis and modelling of data running through every aspect of life. Cutting-edge research now sits at the interface of data science and mathematical modelling. Methods and fields such as compressed sensing, stochastic optimisation, neural networks, Bayesian hierarchical models - to name but a few - have become interwoven and contributed to the delivery of a new domain of research. We refer to this research interface as "statistical applied mathematics". Established in 2014, the Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa, samba.ac.uk) delivers leading research and training in this space. In the development of this bid, we have consulted widely with academic, industrial, and governmental partners, who consistently report a large and widening gap between demand and supply for highly skilled graduates. Our vision is to create a new generation of statistical applied mathematicians ready to lead high-impact, data-driven, mathematically-robust research in academia and industry. We will nurture a vibrant culture of cohort learning, enabling internationally-leading training in modern mathematical data science. A particularly important research focus will be the synthesis of data-driven methods with robust mathematical modelling frameworks. Tomorrow's industrial mathematicians and statisticians must understand when machine learning tools are (and are not) appropriate to use and be able to conduct the underpinning research to improve these tools by integrating scientific domain knowledge. This research challenge is informed by deep partnerships with a range of industry and government bodies. Our long-term partners such as BT, Syngenta, Novartis, the NHS, and the Environment Agency co-create our vision and our training. They are emphatic that we must address the urgent need for mathematical data science talent in this key strategic area for the UK economy. Many of our students will work directly on industry challenges during their PhD either in their core research or with internships. Our unique Integrative Think Tanks are the key mechanism for exploring new research ideas with industry. These are week-long events where SAMBa students, leading academics, and partners work together on industrial and societal problems. SAMBa graduates will be able to develop and apply new ideas and methods to harness the power of data to tackle challenges affecting society, the economy, and the environment. Our students will move into academia, providing sustainability to the UK's capacity in this field, as well as industry and government, providing impact through societal benefits and driving economic growth. Many alumni now hold permanent positions at leading UK universities and senior positions in a range of businesses. The CDT will be embedded within the University of Bath's Department of Mathematical Sciences, where 98% of the research is world leading or internationally excellent (REF2021). The CDT is supported by 58 academics in maths, with similar numbers of co-supervisors from industry and other departments. The centre will be co-delivered with 22 industry and government partners. A vital international perspective is provided by a worldwide network of 11 academic institutions sharing our scientific vision.

Artificial intelligence (AI) is revolutionizing our world by predicting future behaviours from large datasets. Recent excitement has grown around AI that requires small (<100) datasets, guiding the investigation of vital areas like pharmaceuticals. "Active learning" (AL) techniques use experiment outcomes to make recommendations for new experiment designs based on areas of the state space where it is less certain of its predictions. The results of these predictions feed into the model for continual improvement. Bayesian Optimisation is being explored for material discovery tasks, however this process is limited in that models attempt to find the optimal material given a target profile, compared to AL, which focusses on building a robust and interpretable model. This project will aim to develop an inexpensive robot formulator with AL-driven decision-making to accelerate medicine manufacture. It is envisioned that a robot that is able to perform routine laboratory tasks, such as handling liquids and taking analytical measurements, could be guided by a regression AL algorithm such that it not only performs tasks, but learns and executes the next logical step, ultimately developing high quality, safe, and efficacious liquid medicines. Integrating AI, robotics, and automated analysis is an enormous challenge, however the outcomes could be phenomenal. Robotic formulators could drive drug candidates through pharmaceutical bottlenecks rapidly with quality data, using a large design space, with little waste. This will be demonstrated in the project by challenging the robot with complex drugs which are likely to be core medicines of the future. It is envisioned that this approach will be able to identify complex and unintuitive combinations of drug and additives which traditional formulation approaches would not. It is anticipated that the project will have step-wise impact on future innovations. The robot formulator is inexpensive in comparison to current robotic formulation streams (such as those used in the Materials Innovation Factory) and the algorithms can be run on standard PCs using open-source software. Thus, the approach can be adopted in lower-resource environments for local priority medicines. The focus on algorithm integration timely to make best use of recent regression AL principles, and the blueprint proposed amenable to future developments in AI. In order to achieve the ambitious aims of this project, the following process will be followed. Firstly, an inexpensive liquid-handling robot (£9k, owned by the PI) will be instructed to develop mixtures of drug and additive (in solution) with a single read-out (e.g. absorbance). An Xarm 5 robotic arm will be interfaced with the liquid-handling robot to allow the formulations to be transferred into analytical instruments. A regression AL algorithm will then analyse which conditions led to solubility and generate predictions on formulations with improved solubility that the robot will automatically investigate. This process will be optimised and evaluated to demonstrate that the robot is "learning" how to make these medicines better. The study will then move on to exploration of multiple product attributes at the same time, akin to "real world" medicine formulation. The project will match processes the robot performs to those used by industry, to ensure the findings are translatable, guided by collaboration with Bayer. Furthermore, the technology will be designed to use industry-standard software, QBDvision, for high-quality handling and reporting of data. Thus, the robot scientist also provides immaculate reporting of results that are needed for approval of new medicines.