Application of bayesian optimization in magnetic horn design

Bayesian optimization is an effective method for designing complex systems with costly, non-analytic black box objective functions. It enables efficient exploration of the parameter space, making it well-suited for challenging problems in accelerator design which involve computationally intensive simulations such as FLUKA. This study presents a framework to apply Bayesian optimization techniques to design the magnetic horn of Neutrinos from Stored Muons (nuSTORM) experiment for increased pion capture. The optimization process spans a wide range of operational energies, from 1 to 7 GeV, to address the physics reach of nuSTORM. Batch sampling is enabled through specialized acquisition functions, allowing simulations to run in parallel across a computational cluster and significantly reducing the time needed to identify optimal target and horn configurations for the muon source. By leveraging the surrogate models generated through Bayesian optimization, horn configurations at different energies are systematically compared. This facilitates sensitivity studies to determine a minimal set of horn designs that efficiently cover the nuSTORM kinematic range.