# Learning to Simulate: Generative Metamodeling via Quantile Regression

arXiv: https://arxiv.org/abs/2311.17797 · HTML: https://mlsanity.com/paper/2311.17797/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 61 references that are in the map.
- First posted on arXiv 29 Nov 2023.

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [Using Wasserstein Generative Adversarial Networks for the Design of Monte Carlo Simulations](https://mlsanity.com/paper/1909.02210/) (2019)
- [Autoregressive Quantile Networks for Generative Modeling](https://mlsanity.com/paper/1806.05575/) (2018)
- [Deep Generative Quantile-Copula Models for Probabilistic Forecasting](https://mlsanity.com/paper/1907.10697/) (2019)
- [Probabilistic Time Series Forecasting with Implicit Quantile Networks](https://mlsanity.com/paper/2107.03743/) (2021)
- [Ranking and Selection with Covariates for Personalized Decision Making](https://mlsanity.com/paper/1710.02642/) (2017)
- [Efficient Learning for Clustering and Optimizing Context-Dependent Designs](https://mlsanity.com/paper/2012.05591/) (2020)
- [Continuous Conditional Generative Adversarial Networks (cGAN) with Generator Regularization](https://mlsanity.com/paper/2103.14884/) (2021)
- [Non-crossing convex quantile regression](https://mlsanity.com/paper/2204.01371/) (2022)

## Built on by (most cited first, 3 of 3)

- [Generative Conditional Distributions by Neural (Entropic) Optimal Transport](https://mlsanity.com/paper/2406.02317/) (2024)
- [Conditional Generative Modeling for Enhanced Credit Risk Management in Supply Chain Finance](https://mlsanity.com/paper/2506.15305/) (2025)
- [E-QRGMM: Efficient Generative Metamodeling for Covariate-Dependent Uncertainty Quantification](https://mlsanity.com/paper/2601.19256/) (2026)

## Abstract (arXiv)

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.