Bayesian Optimisation with Dimensionless Groups: A Synergy of Performance and Fundamental Understanding

Dimensionless groups quantify the balance among key forces governing a system’s physical behaviour and are foundational in engineering for describing, comparing, and scaling processes. By condensing complex system interactions into single values, they provide a powerful means of abstraction. Yet, their potential to actively guide process optimisation remains largely untapped. This study presents a framework that integrates dimensionless analysis with Bayesian optimisation to enhance both process performance and interpretability. Using this combined approach, we demonstrate that optimisation conducted in the dimensionless space not only accelerates convergence towards optimal process conditions but also reveals the underlying physical balances driving system behaviour. The method thus bridges data-driven optimisation with physically grounded understanding, enabling more efficient and explainable control of complex manufacturing processes.