🤖 AI Summary
Conventional metamodeling is constrained by pre-specified single-output statistics (e.g., mean), limiting its applicability in real-time decision-making where arbitrary statistics must be computed on demand. Method: We propose a generative metamodeling paradigm—designed to serve as a fast surrogate for simulators—that efficiently generates random samples approximating the true conditional distribution given any input. To this end, we formally define generative metamodeling and introduce Quantile Regression-based Generative Metamodeling (QRGMM), a novel algorithm grounded in quantile regression. We provide theoretical guarantees on its conditional distribution convergence and establish its optimal convergence rate. Results: Experiments across diverse real-time decision tasks demonstrate that QRGMM significantly outperforms existing generative models: it achieves 100×–1000× faster inference while preserving high distributional fidelity, thereby overcoming the flexibility bottleneck inherent in traditional single-statistic surrogates.
📝 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 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.