  Dynamic aperture is an important concept for the study of non-linear beam
dynamics in circular accelerators. It describes the extent of the phase-space
region where a particle's motion remains bounded over a given number of turns.
Understanding the features of dynamic aperture is crucial for the design and
operation of such accelerators, as it provides insights into nonlinear effects
and the possibility of optimising beam lifetime. The standard approach to
calculate the dynamic aperture requires numerical simulations of several
initial conditions densely distributed in phase space for a sufficient number
of turns to probe the time scale corresponding to machine operations. This
process is very computationally intensive and practically outside the range of
today's computers. In our study, we introduced a novel method to estimate
dynamic aperture rapidly and accurately by utilising a Deep Neural Network
model. This model was trained with simulated tracking data from the CERN Large
Hadron Collider and takes into account variations in accelerator parameters
such as betatron tune, chromaticity, and the strength of the Landau octupoles.
To enhance its performance, we integrate the model into an innovative Active
Learning framework. This framework not only enables retraining and updating of
the computed model, but also facilitates efficient data generation through
smart sampling. Since chaotic motion cannot be predicted, traditional tracking
simulations are incorporated into the Active Learning framework to deal with
the chaotic nature of some initial conditions. The results demonstrate that the
use of the Active Learning framework allows faster scanning of the
configuration parameters without compromising the accuracy of the dynamic
aperture estimates.
