Abstract: Large-scale stochastic mechanistic models are more and more used in recent years to model global epidemic outbreaks and are useful tool for policy and decision makers to project, forecast, and asses the impact of epidemics. However, these models are incredibly demanding from a computational standpoint and time-consuming to run. Here, we present GLEAM-AI, a spatio-temporal probabilistic neural surrogate model to replicate the insights and results of large-scale mechanistic epidemic models and to accelerate stochastic simulations. We show how a surrogate model can efficiently be trained with less than $5.3$ thousand simulations from the mechanistic model by utilizing a Bayesian active learning approach. We demonstrate its performance in efficiently replicating the mechanistic dynamics, providing approximately a $200$ times speed-up with respect to the original model.