Stochastic simulation models, while effective in capturing the dynamics of complex systems, are often too slow to run for real-time decision-making. Metamodeling techniques are widely used to learn the relationship between a summary statistic of the outputs (e.g., the mean or quantile) and the inputs of the simulator, so that it can be used in real time. However, this methodology requires the knowledge of an appropriate summary statistic in advance, making it inflexible for many practical situations. In this paper, we propose a new metamodeling concept, called generative metamodeling, which aims to construct a "fast simulator of the simulator". This technique can generate random outputs substantially faster than the original simulation model, while retaining an approximately equal conditional distribution given the same inputs. Once constructed, a generative metamodel can instantaneously generate a large amount of random outputs as soon as the inputs are specified, thereby facilitating the immediate computation of any summary statistic for real-time decision-making. Furthermore, we propose a new algorithm -- quantile-regression-based generative metamodeling (QRGMM) -- and study its convergence and rate of convergence. Extensive numerical experiments are conducted to investigate the empirical performance of QRGMM, compare it with other state-of-the-art generative algorithms, and demonstrate its usefulness in practical real-time decision-making.

翻译：随机仿真模型虽能有效捕捉复杂系统的动态特性，但往往因运行速度过慢而无法用于实时决策。元建模技术被广泛用于学习输出摘要统计量（如均值或分位数）与仿真器输入之间的关系，从而支持实时应用。然而，该方法需要预先指定合适的摘要统计量，这在许多实际场景中缺乏灵活性。本文提出一种名为生成式元建模的新概念，旨在构建一个"仿真器的快速仿真器"。该技术能在保持与原仿真模型近似相同的条件分布的前提下，以显著快于原始模型的速度生成随机输出。生成式元模型构建完成后，一旦输入指定即可瞬时生成大量随机输出，从而支持实时决策中任意摘要统计量的即时计算。此外，我们提出了一种新算法——基于分位数回归的生成式元建模（QRGMM），并研究了其收敛性与收敛速率。通过大量数值实验，我们检验了QRGMM的实证性能，并将其与其他主流生成式算法进行对比，同时展示了其在实时决策中的实际应用价值。