My research is centred around knowledge modelling for manufacturing, encompassing various areas such as smart information systems, abstract mathematical theory (category theory), Geometrical Product Specifications and Verification (GPS), Additive Manufacturing (AM), surface design, and metrology. It is a multidisciplinary endeavour, bridging mathematics, informatics, manufacturing, and measurement science. Over the course of 13 years, I have been devoted to developing smart decision-making tools for product design and inspection using category theory as the foundational mathematical language. This approach offers a promising solution to handling vast and diverse datasets for autonomous decision-making in digital manufacturing.

The origins of my research interest stem from developing intelligent information systems for geometrical product design, manufacturing, and measurement. These systems aim to help designers, manufacturers, and inspectors comply with extensive guidelines and rules set by national/international standards. Previously, object-oriented languages served as the basis for development tools, but they proved inadequate when dealing with large amounts of structured data, requiring consistent updates and revisions. The search for a suitable solution led to the discovery of an abstract mathematical theory - category theory, which has been instrumental in simplifying complex relationships and enabling better decision-making in this context.

In the early years, my research took a unique and less-explored path, centred in the abstract and lesser-known realm of category theory, which initially received limited recognition from the engineering society. However, as manufacturing continues to embrace a vast array of advancing digital technologies, the landscape is evolving towards smarter and more complex systems. These advancements, including cyber-physical systems, internet of things, cloud computing, cognitive computing, and artificial intelligence, are driving digital manufacturing towards higher levels of abstraction. As a result, managing multiple levels of abstraction has become increasingly complex, necessitating the integration of various siloed abstraction technologies, such as databases, ontology, and machine learning, through ad-hoc intermediate models. The application of multi-level abstraction becomes paramount to address this profound challenge. This importance is echoed in Machine Learning as well, as highlighted by Dr. Yann LeCun, a pioneer in deep learning. He highlights the need for hierarchical learning at multiple levels of abstraction and time scales to overcome the limitations of current ML.

My research aims to develop foundations and tools to make digital systems simpler, and support smarter decision-making in future digital manufacturing. I'm taking a broad approach intentionally because the foundations and tools we create won't just be useful in manufacturing. The universal utility of categorical semantics, which is structured based on category theory, also opens up many possibilities for using it in various fields, such as engineering, smart cities, and healthcare.

The research will try to find solutions to the following questions:

• How can we create a ‘better’ digital world for manufacturing?
• How can we understand and manage communication across digital models effectively?
• How can we and machines make timely and informed decisions?
• How can we implement these solutions in practical application?