Uncertainty-Quantified Machine Model Construction Using Physics-Informed Gaussian Processes and Bayesian Optimization

To construct a closed orbit model for an accelerator ring with intrinsic uncertainty quantification from orbit measurements, a physics-informed Gaussian Process model is proposed based on a stochastic ensemble of MAD-X lattices. Key advantages compared to LOCO (Linear Optics from Closed Orbits) include (1.) uncertainty-enabled orbit prediction in between BPMs (beam position monitors), (2.) fitting of a parameter distribution (dipole-like field errors) which inherently models uncertainty, (3.) incorporation of measurement uncertainty from BPM noise, and (4.) an active learning approach which can be more sample efficient than measuring an orbit response matrix. A case study is presented for the GSI heavy ion synchrotron SIS18 with various simulated applications, in particular constructing an effective machine model with minimal orbit uncertainty around the ring, and orbit correction to achieve minimal deviation at a specific location such as, e.g., the septum to control beam loss during slow extraction. This physics-inspired Gaussian Process regression approach shows potential to be applied to optics correction and further applications beyond closed orbit correction.