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.

翻译：大规模、时空、年龄结构的流行病模型等随机模拟在精细分辨率下计算成本高昂。虽然深度替代模型可以加速模拟，但针对随机模拟并结合主动学习方法的研究尚不充分。我们提出交互式神经过程（INP），这是一种用于学习深度替代模型以加速随机模拟的深度贝叶斯主动学习框架。INP由两部分组成：基于神经过程（NP）家族的时空替代模型和用于主动学习的采集函数。在替代建模方面，我们开发了时空神经过程（STNP）以模拟模拟器的动态行为。在主动学习方面，我们提出了一种新的采集函数——潜信息增益（LIG），该函数在基于NP模型的潜空间中计算。我们进行了理论分析，证明在高维情况下，LIG相比随机采样降低了样本复杂度。我们还在反应扩散、热流和传染病三种复杂的时空模拟器上进行了实证研究。结果表明，STNP在离线学习场景中优于基线方法，而LIG在贝叶斯主动学习领域达到了最优性能。