Advances in machine learning inference of dynamic aperture evaluation for the LHC

Dynamic aperture (DA) is a crucial metric for understanding nonlinear beam dynamics and particle stability in circular accelerators like the Large Hadron Collider (LHC) and its future High-Luminosity LHC (HL-LHC) upgrade. Traditional methods for DA evaluation are computationally intensive, requiring extensive tracking of large particle ensembles over many turns. Recent advances in machine learning (ML) have shown that models, particularly architectures like Bidirectional Encoder Representations from Transformers (BERT), can significantly accelerate DA predictions while achieving accuracies comparable to traditional simulations. Enhanced uncertainty quantification techniques further improve model reliability, providing a foundation for robust active learning frameworks. This work presents the latest progress in DA inference, focusing on architectural advances, data preparation, and optimised training techniques. Applied to LHC tracking data, these improvements highlight the importance of high-quality data generation and customised training strategies for enhancing model performance and uncertainty management, paving the way for future HL-LHC studies.