Bayesian stellarator coil design

We present a Bayesian method for designing coil filaments for stellarator configurations, formulating the problem as the exploration of the posterior distribution over filament shapes conditioned on a target magnetic field. The magnetic field generated by a candidate coil set is compared with the target field using the predictive probability. Additional constraints, such as penalties on coil length and curvature, are incorporated into the prior through virtual observations. In contrast to conventional methods that rely on heuristic tuning, our approach infers hyperparameters, including the weights associated with these constraints, automatically by exploring the joint posterior over coil filaments and hyperparameters. This follows the principle of Occam's razor, balancing geometric simplicity with magnetic field accuracy. The outcome is a set of coil filaments that reproduce the target field with acceptable deviations while avoiding unnecessary complexity. The method also quantifies posterior uncertainty in filament geometry and adaptively tunes all weight parameters for each stellarator configuration. By systematically integrating prior knowledge and quantifying uncertainty, the framework provides a principled, robust and flexible approach to coil design in stellarator optimisation.