Stochastic simulation models effectively capture complex system dynamics but are often too slow for real-time decision-making. Traditional metamodeling techniques learn relationships between simulator inputs and a single output summary statistic, such as the mean or median. These techniques enable real-time predictions without additional simulations. However, they require prior selection of one appropriate output summary statistic, limiting their flexibility in practical applications. We propose a new concept: generative metamodeling. It aims to construct a "fast simulator of the simulator," generating random outputs significantly faster than the original simulator while preserving approximately equal conditional distributions. Generative metamodels enable rapid generation of numerous random outputs upon input specification, facilitating immediate computation of any summary statistic for real-time decision-making. We introduce a new algorithm, quantile-regression-based generative metamodeling (QRGMM), and establish its distributional convergence and convergence rate. Extensive numerical experiments demonstrate QRGMM's efficacy compared to other state-of-the-art generative algorithms in practical real-time decision-making scenarios.

翻译：随机仿真模型能有效捕捉复杂系统动态，但通常因计算速度过慢而难以支持实时决策。传统元建模技术旨在学习仿真器输入与单一输出汇总统计量（如均值或中位数）之间的关系，从而无需额外仿真即可实现实时预测。然而，这些方法需要预先选定合适的输出汇总统计量，限制了实际应用的灵活性。本文提出一种新范式：生成式元建模。其目标是构建"仿真器的快速仿真器"，在保持近似相等的条件分布前提下，以远高于原始仿真器的速度生成随机输出。生成式元模型可在输入指定后快速生成大量随机输出，从而即时计算任意汇总统计量以支持实时决策。我们提出一种新算法——基于分位数回归的生成式元建模（QRGMM），并证明其分布收敛性及收敛速率。大量数值实验表明，在实际实时决策场景中，QRGMM相较于其他前沿生成算法具有显著优势。