# Generation of non-stationary stochastic fields using Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2205.05469 · HTML: https://mlsanity.com/paper/2205.05469/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 11 May 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Semantic Image Synthesis with Spatially-Adaptive Normalization](https://mlsanity.com/paper/1903.07291/) (2019)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [Training-image based geostatistical inversion using a spatial generative adversarial neural network](https://mlsanity.com/paper/1708.04975/) (2017)
- [Parametric generation of conditional geological realizations using generative neural networks](https://mlsanity.com/paper/1807.05207/) (2018)
- [Generating Realistic Geology Conditioned on Physical Measurements with Generative Adversarial Networks](https://mlsanity.com/paper/1802.03065/) (2018)
- [Parametrization and generation of geological models with generative adversarial networks](https://mlsanity.com/paper/1708.01810/) (2017)
- [Discovering state-parameter mappings in subsurface models using generative adversarial networks](https://mlsanity.com/paper/1810.12856/) (2018)
- [Rapid seismic domain transfer: Seismic velocity inversion and modeling using deep generative neural networks](https://mlsanity.com/paper/1805.08826/) (2018)
- [Parametrization of stochastic inputs using generative adversarial networks with application in geology](https://mlsanity.com/paper/1904.03677/) (2019)
- [Generating unrepresented proportions of geological facies using Generative Adversarial Networks](https://mlsanity.com/paper/2203.09639/) (2022)

## Abstract (arXiv)

In the context of generating geological facies conditioned on observed data, samples corresponding to all possible conditions are not generally available in the training set and hence the generation of these realizations depends primary on the generalization capability of the trained generative model. The problem becomes more complex when applied on non-stationary fields. In this work, we investigate the problem of using Generative Adversarial Networks (GANs) models to generate non-stationary geological channelized patterns and examine the models generalization capability at new spatial modes that were never seen in the given training set. The developed training method based on spatial-conditioning allowed for effective learning of the correlation between the spatial conditions (i.e. non-stationary maps) and the realizations implicitly without using additional loss terms or solving optimization problems for every new given data after training. In addition, our models can be trained on 2D and 3D samples. The results on real and artificial datasets show that we were able to generate geologically-plausible realizations beyond the training samples and with a strong correlation with the target maps.