  Stochastic simulations such as large-scale, spatiotemporal, age-structured
epidemic models are computationally expensive at fine-grained resolution. While
deep surrogate models can speed up the simulations, doing so for stochastic
simulations and with active learning approaches is an underexplored area. We
propose Interactive Neural Process (INP), a deep Bayesian active learning
framework for learning deep surrogate models to accelerate stochastic
simulations. INP consists of two components, a spatiotemporal surrogate model
built upon Neural Process (NP) family and an acquisition function for active
learning. For surrogate modeling, we develop Spatiotemporal Neural Process
(STNP) to mimic the simulator dynamics. For active learning, we propose a novel
acquisition function, Latent Information Gain (LIG), calculated in the latent
space of NP based models. We perform a theoretical analysis and demonstrate
that LIG reduces sample complexity compared with random sampling in high
dimensions. We also conduct empirical studies on three complex spatiotemporal
simulators for reaction diffusion, heat flow, and infectious disease. The
results demonstrate that STNP outperforms the baselines in the offline learning
setting and LIG achieves the state-of-the-art for Bayesian active learning.
