Categorical Batch Bayesian Optimisation for High-Dimensional Design in Particle-Laden Flows

Geometries can be parameterised in multiple ways, and they strongly influence performance in biomedical, energy or transport systems. However, optimisation workflows often rely on a single, simplified parameterisation to reduce dimensionality. While this keeps optimisation tractable and lowers computational costs, it limits exploration of complex geometries and can miss high-performance designs. Even Bayesian Optimisation (BO), widely used in design tasks, becomes less effective beyond Θ Є ℝ¹⁰, making it poorly suited for high-dimensional, multi-parameterisation spaces. To address these challenges, we extend Categorical Bayesian Optimisation (CBO), applied to materials [1] and machine learning hyperparameters, to develop a Categorical Batch Bayesian Optimisation (CBBO) framework for shape optimisation. This is the first application of CBO for design, where each category represents a fundamentally different parameterisation with distinct geometric expressivity. We apply CBBO to optimise geometries in 2D particle-laden flows with rigid-body motion, Eulerian particle transport, and level-set methods to track deposit evolution across different motion regimes. Simulations run over long timescales (100 s), with the objective of minimising average deposition rates on the object surface. CBBO simultaneously selects and optimises across parameterisations: (1) Non-uniform rational basis spline (NURBS) with polar/Cartesian jitter (Θ Є ℝ³³), (2) GP-interpolated radial profiles (Θ Є ℝ⁷), and symmetric NURBS (Θ Є ℝ⁶). CBBO outperforms standard BO on single parameterisations, discovering airfoil-like profiles for translation, symmetric shapes for rotation, and complex designs for compound motion while achieving lower deposition with fewer simulations. By eliminating the need for human expertise in pre-selecting parameterisations for different motion regimes, CBBO opens new possibilities for automated, physics-aware shape optimisation in complex fluid systems and beyond.

[1] F. Häse et al. Applied Physics Reviews, vol. 8, no. 3, p. 031406, Sep. 2021.

[2] X. Wan et al. Proceedings of the 38th ICML, 2021.