This study investigates the quantification of uncertainty in the buckling behavior of imperfect spherical shells subjected to external pressure and examines the sensitivity of parameters influencing the critical buckling load. In this framework, initial geometric imperfections, thickness variations, variations in material mechanical properties, and boundary condition uncertainties are considered as the primary sources of uncertainty in the model. The numerical results indicate that increasing the shell thickness leads to a nonlinear increase in the critical buckling load, whereas an increase in the amplitude of geometric imperfections has the most significant contribution to the reduction of buckling capacity. Furthermore, variations in elastic material properties and boundary conditions can result in shifts in buckling modes and changes in the instability mechanism. Sensitivity analysis reveals that the geometric imperfection amplitude and the thickness-to-radius ratio are the dominant parameters governing the buckling behavior of spherical shells. In the second stage, a multilayer perceptron artificial neural network was employed for rapid modeling and prediction of buckling behavior. Data obtained from the numerical analyses were used as the training and testing datasets for the network. The results demonstrate that the neural network model is capable of predicting the critical buckling load and dominant instability mode with satisfactory accuracy and shows a strong correlation with finite element analysis results. These findings indicate that combining nonlinear numerical analysis with artificial intelligence-based modeling provides an efficient framework for reliability-based design of imperfect spherical shells and significantly reduces computational time without compromising prediction accuracy.