Interpretable Surrogate Modelling for Multirotor Design Exploration: Combining HDMR and Kolmogorov–Arnold Decomposition

Multirotor unmanned aerial vehicles increasingly require design optimisation balancing aerodynamic efficiency, noise emissions, and operational constraints. While machine learning surrogates enable rapid performance prediction, their opacity limits physical insight into how design variables, such as rotor speed, blade pitch, and geometry, interact to shape system behaviour. For safety-critical applications, this lack of transparency complicates certification and informed design decisions. This work presents a framework combining High Dimensional Model Representation (HDMR) and Kolmogorov–Arnold Modelling (KAM) to extract interpretable structure from rotor aerodynamic performance models.

HDMR provides variance-based sensitivity indices and quantifies parameter interactions through additive decomposition. KAM complements this with a compositional representation that identifies localised functional regimes and reveals how variable importance shifts across the design space. The methodology is first validated on analytical benchmark functions exhibiting tuneable interaction structures, then applied to a parametric study of rotor thrust and efficiency generated using a mid-fidelity vortex particle method. The framework provides a foundation for extending the analysis to multi-rotor configurations where parameter interactions become increasingly complex.

The results will demonstrate how HDMR effectively ranks dominant parameters globally, while KAM uncovers regime transitions corresponding to shifts in dominant parameter interactions across the design space. The combined approach supports transparent design exploration and provides a starting point for regime-aware optimisation strategies in multirotor development.