Beam-based identification of magnetic field errors in a synchrotron using deep Lie map networks

We report on the recovery of both linear and nonlinear optics in a hadron synchrotron using the novel deep Lie map network (DLMN) approach. The DLMN enables the construction of a detailed accelerator model by integrating charged particle dynamics with machine learning methods within a data-driven framework. The primary observable is the centroid motion over a limited number of turns, captured by beam position monitors. The DLMN generates an updated description of the accelerator in terms of magnetic multipole components, which can be directly utilized in established accelerator physics tools and tracking codes for further analysis. In this study, the DLMN approach is employed to recover a linear optics model, including gradient errors, from a single measured trajectory. Nonlinear optics, including sextupole errors, are recovered using three measured trajectories. We assess the validity of these results by comparison with the linear optics from closed orbits algorithm and through estimates of resonance driving terms. Additionally, we illustrate an application of the deep Lie map network and the predicted synchrotron optics by comparing measured and simulated tune scans.