Topological-based numerical methods for real-world problems

这个项目建议使用数值方法，特别是结合拓扑技术的方法，来调查一系列复杂的跨学科研究问题。这将涉及与现有合作伙伴合作，并与研究团体和行业建立新的伙伴关系，为现实世界的问题创造创新的解决方案。该项目将继续进行三个关键的现有合作：心血管科学研究所--通过使用拓扑学数值方法在生物医学光学领域推进光声成像技术。雷尼绍公司。-使用拓扑机器学习提高光谱仪的灵敏度。6比特教育有限公司-使用拓扑树上的机器学习来探索学生作业中的相似性度量。此外，该项目将寻求与化学学院软材料计算和理论系的新合作，在那里将采用数值和数学方法来研究软材料。本博士的主要目标是创建基于拓扑学方法的数值工具包和库，以解决各种研究问题。这些问题的解决方案将产生现实世界的影响，并可能在不久的将来实施。运营几个迷你项目和行业安置的方法允许实践学习，并有机会向具有不同专业领域的其他群体学习。该项目为在许多领域取得突破性进展提供了极大的机会。

This project proposes to use numerical methods, specifically methods incorporating topological techniques, to investigate a range of complex interdisciplinary research problems. This will involve working with existing partners and creating new partnerships with research groups and industries to create innovative solutions to real-world problems. There are three key existing collaborations which this project will continue: The institute of Cardiovascular Sciences - Advancing photoacoustic imaging technologies within the biomedical optics sector by employing topological numerical methods. Renishaw plc. - Improving the sensitivity of spectrometers using topological machine learning. 6 Bit Education Ltd. - Improbing the similarity measures in student assignments using machine learning on topological trees. Additionally, this project will seek a new collaboration with the Computation and Theory of Soft Materials department within the School of Chemistry, where numerical and mathematical methods will be implemented to study soft materials. The main goal of this PhD is to create numerical toolkits and libraries based on topological methods to solve a variety of research problems. The solutions to these problems will have a real-world impact and could be implement in the near future. The approach of running several mini projects along with industry placements allows for hands-on learning and opportunities to learn from other groups of people with different areas of expertise. This project offers great chances for groundbreaking advancements in many fields.