The dynamic aperture is an essential concept in circular particle accelerators, providing the extent of the phase space region where particle motion remains stable over multiple turns. The accurate prediction of the dynamic aperture is key to optimising performance in accelerators such as the CERN Large Hadron Collider and is crucial for designing future accelerators like the CERN Future Circular Hadron Collider. Traditional methods for computing the dynamic aperture are computationally demanding and involve extensive numerical simulations with numerous initial phase space conditions. In our recent work, we have devised surrogate models to predict the dynamic aperture boundary both efficiently and accurately. These models have been further refined by incorporating them into a novel active learning framework. This framework enhances performance through continual retraining and intelligent data generation based on informed sampling driven by error estimation. A critical attribute of this framework is the precise estimation of uncertainty in dynamic aperture predictions. In this study, we investigate various machine learning techniques for uncertainty estimation, including Monte Carlo dropout, bootstrap methods, and aleatory uncertainty quantification. We evaluated these approaches to determine the most effective method for reliable uncertainty estimation in dynamic aperture predictions using machine learning techniques.
Montanari et al. (Fri,) studied this question.