Understanding the concept of dynamic aperture provides essential insights into nonlinear beam dynamics, beam losses, and the beam lifetime in circular particle accelerators. This comprehension is crucial for the functioning of modern hadron synchrotrons like the CERN Large Hadron Collider and the planning of future ones such as the Future Circular Collider. The dynamic aperture defines the extent of the region in phase space where the trajectories of charged particles are bounded over numerous revolutions, the actual number being defined by the physical application. Traditional methods for calculating the dynamic aperture depend on computationally demanding numerical simulations, which require tracking over multiple turns of numerous initial conditions appropriately distributed in phase space. Prior research has shown the efficiency of a multilayer perceptron network in forecasting the dynamic aperture of the CERN Large Hadron Collider ring, achieving a remarkable speed-up of up to 200-fold compared to standard numerical tracking tools. Building on recent advancements, we conducted a comparative study of various deep learning networks based on BERT, DenseNet, ResNet and VGG architectures. The results demonstrate substantial enhancements in the prediction of the dynamic aperture, marking a significant advancement in the development of more precise and efficient surrogate models of beam dynamics.