# Adversarial sampling of unknown and high-dimensional conditional distributions

arXiv: https://arxiv.org/abs/2111.05962 · HTML: https://mlsanity.com/paper/2111.05962/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 98 references that are in the map.
- First posted on arXiv 8 Nov 2021.

## Builds on (most cited first, 30 of 31)

- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Toward Multimodal Image-to-Image Translation](https://mlsanity.com/paper/1711.11586/) (2017)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Energy-based Generative Adversarial Network](https://mlsanity.com/paper/1609.03126/) (2016)
- [Diversity-Sensitive Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1901.09024/) (2019)
- [Amortised MAP Inference for Image Super-resolution](https://mlsanity.com/paper/1610.04490/) (2016)
- [Stacked Generative Adversarial Networks](https://mlsanity.com/paper/1612.04357/) (2016)
- [AdaGAN: Boosting Generative Models](https://mlsanity.com/paper/1701.02386/) (2017)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [Deep Learning the Physics of Transport Phenomena](https://mlsanity.com/paper/1709.02432/) (2017)
- [Is Generator Conditioning Causally Related to GAN Performance?](https://mlsanity.com/paper/1802.08768/) (2018)
- [Turbulence Enrichment using Physics-informed Generative Adversarial Networks](https://mlsanity.com/paper/2003.01907/) (2020)
- [Physics-Informed Neural Network Super Resolution for Advection-Diffusion Models](https://mlsanity.com/paper/2011.02519/) (2020)
- [From Deep to Physics-Informed Learning of Turbulence: Diagnostics](https://mlsanity.com/paper/1810.07785/) (2018)
- [MTAdam: Automatic Balancing of Multiple Training Loss Terms](https://mlsanity.com/paper/2006.14683/) (2020)
- [Encoding Invariances in Deep Generative Models](https://mlsanity.com/paper/1906.01626/) (2019)

## Built on by (most cited first, 13 of 13)

- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning](https://mlsanity.com/paper/2302.06186/) (2023)
- [Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks](https://mlsanity.com/paper/2409.07769/) (2024)
- [PINN surrogate of Li-ion battery models for parameter inference. Part II: Regularization and application of the pseudo-2D model](https://mlsanity.com/paper/2312.17336/) (2023)
- [Ensemble flow reconstruction in the atmospheric boundary layer from spatially limited measurements through latent diffusion models](https://mlsanity.com/paper/2303.00836/) (2023)
- [Uniform-in-Phase-Space Data Selection with Iterative Normalizing Flows](https://mlsanity.com/paper/2112.15446/) (2021)
- [Statistical treatment of convolutional neural network super-resolution of inland surface wind for subgrid-scale variability quantification](https://mlsanity.com/paper/2211.16708/) (2022)
- [Jacobian-Scaled K-means Clustering for Physics-Informed Segmentation of Reacting Flows](https://mlsanity.com/paper/2305.01539/) (2023)
- [Swift Hydra: Self-Reinforcing Generative Framework for Anomaly Detection with Multiple Mamba Models](https://mlsanity.com/paper/2503.06413/) (2025)
- [Patch-Based 3D Variational Autoencoder for Super-Resolution of Turbulent Channel Flow](https://mlsanity.com/paper/2507.22082/) (2025)
- [GANISP: a GAN-assisted Importance SPlitting Probability Estimator](https://mlsanity.com/paper/2112.15444/) (2021)
- [A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks](https://mlsanity.com/paper/2402.18729/) (2024)
- [Neural posterior estimation for scalable and accurate inverse parameter inference in Li-ion batteries](https://mlsanity.com/paper/2604.02520/) (2026)

## Abstract (arXiv)

Many engineering problems require the prediction of realization-to-realization variability or a refined description of modeled quantities. In that case, it is necessary to sample elements from unknown high-dimensional spaces with possibly millions of degrees of freedom. While there exist methods able to sample elements from probability density functions (PDF) with known shapes, several approximations need to be made when the distribution is unknown. In this paper the sampling method, as well as the inference of the underlying distribution, are both handled with a data-driven method known as generative adversarial networks (GAN), which trains two competing neural networks to produce a network that can effectively generate samples from the training set distribution. In practice, it is often necessary to draw samples from conditional distributions. When the conditional variables are continuous, only one (if any) data point corresponding to a particular value of a conditioning variable may be available, which is not sufficient to estimate the conditional distribution. This work handles this problem using an a priori estimation of the conditional moments of a PDF. Two approaches, stochastic estimation, and an external neural network are compared here for computing these moments; however, any preferred method can be used. The algorithm is demonstrated in the case of the deconvolution of a filtered turbulent flow field. It is shown that all the versions of the proposed algorithm effectively sample the target conditional distribution with minimal impact on the quality of the samples compared to state-of-the-art methods. Additionally, the procedure can be used as a metric for the diversity of samples generated by a conditional GAN (cGAN) conditioned with continuous variables.