Stochastic simulations such as large-scale, spatiotemporal, age-structured epidemic models are computationally expensive at fine-grained resolution. We propose Interactive Neural Process (INP), a Bayesian active learning framework to proactively learn a deep learning surrogate model and accelerate simulation. Our framework is based on the novel integration of neural process, deep sequence model and active learning. In particular, we develop a novel spatiotemporal neural process model to mimic the simulator dynamics. Our model automatically infers the latent process which describes the intrinsic uncertainty of the simulator. This also gives rise to a new acquisition function based on the latent information gain. We design Bayesian active learning algorithms to iteratively query the simulator, gather more data, and continuously improve the model. We perform theoretical analysis and demonstrate that our approach reduces sample complexity compared with random sampling in high dimension. Empirically, we demonstrate our framework can faithfully imitate the behavior of a complex infectious disease simulator with a small number of examples, enabling rapid simulation and scenario exploration.