Learning to Simulate: Generative Metamodeling via Quantile Regression

Abstract

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. Extensive numerical experiments demonstrate QRGMM’s efficacy compared with other state-of-the-art generative algorithms in practical real-time decision-making scenarios. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This research was partially supported by the National Natural Science Foundation of China [Grant 72091211]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1378 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2025.1378 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .