# Parametrization of stochastic inputs using generative adversarial networks with application in geology

arXiv: https://arxiv.org/abs/1904.03677 · HTML: https://mlsanity.com/paper/1904.03677/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2019.

## Built on by (most cited first, 5 of 5)

- [Generating unrepresented proportions of geological facies using Generative Adversarial Networks](https://mlsanity.com/paper/2203.09639/) (2022)
- [Deep learning for prediction of complex geology ahead of drilling](https://mlsanity.com/paper/2104.02550/) (2021)
- [Generation of non-stationary stochastic fields using Generative Adversarial Networks](https://mlsanity.com/paper/2205.05469/) (2022)
- [Constrained Transformer-Based Porous Media Generation to Spatial Distribution of Rock Properties](https://mlsanity.com/paper/2410.21462/) (2024)
- [Enhancing the Parameterization of Reservoir Properties for Data Assimilation Using Deep VAE-GAN](https://mlsanity.com/paper/2603.18766/) (2026)

## Abstract (arXiv)

We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly constructing a parametric form to preserve predefined statistics of the data. This is done by training a neural network to generate samples from the data distribution using a recent deep learning technique called generative adversarial networks. By emulating the data generating process, the relevant statistics of the data are replicated. The method is assessed in subsurface flow problems, where effective parametrization of underground properties such as permeability is important due to the high dimensionality and presence of high spatial correlations. We experiment with realizations of binary channelized subsurface permeability and perform uncertainty quantification and parameter estimation. Results show that the parametrization using generative adversarial networks is very effective in preserving visual realism as well as high order statistics of the flow responses, while achieving a dimensionality reduction of two orders of magnitude.