# Parametric generation of conditional geological realizations using generative neural networks

arXiv: https://arxiv.org/abs/1807.05207 · HTML: https://mlsanity.com/paper/1807.05207/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2018.

## Built on by (most cited first, 19 of 19)

- [Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solvers](https://mlsanity.com/paper/2207.11417/) (2022)
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- [Generating unrepresented proportions of geological facies using Generative Adversarial Networks](https://mlsanity.com/paper/2203.09639/) (2022)
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- [A stable deep adversarial learning approach for geological facies generation](https://mlsanity.com/paper/2305.13318/) (2023)
- [Stochastic full waveform inversion with deep generative prior for uncertainty quantification](https://mlsanity.com/paper/2406.04859/) (2024)
- [Pix2Geomodel: A Next-Generation Reservoir Geomodeling with Property-to-Property Translation](https://mlsanity.com/paper/2506.17747/) (2025)
- [Differentiable Inverse Modeling with Physics-Constrained Latent Diffusion for Heterogeneous Subsurface Parameter Fields](https://mlsanity.com/paper/2512.22421/) (2025)
- [Deep learning for prediction of complex geology ahead of drilling](https://mlsanity.com/paper/2104.02550/) (2021)
- [Diffusion models for multivariate subsurface generation and efficient probabilistic inversion](https://mlsanity.com/paper/2507.15809/) (2025)
- [3D latent diffusion models for parameterizing and history matching multiscenario facies systems](https://mlsanity.com/paper/2508.16621/) (2025)
- [Generation of non-stationary stochastic fields using Generative Adversarial Networks](https://mlsanity.com/paper/2205.05469/) (2022)
- [History Matching under Uncertainty of Geological Scenarios with Implicit Geological Realism Control with Generative Deep Learning and Graph Convolutions](https://mlsanity.com/paper/2507.10201/) (2025)
- [Statistically Accurate and Robust Generative Prediction of Rock Discontinuities with A Tabular Foundation Model](https://mlsanity.com/paper/2511.13339/) (2025)
- [Leveraging generative adversarial networks with spatially adaptive denormalization for multivariate stochastic seismic data inversion](https://mlsanity.com/paper/2512.02863/) (2025)
- [Enhancing the Parameterization of Reservoir Properties for Data Assimilation Using Deep VAE-GAN](https://mlsanity.com/paper/2603.18766/) (2026)
- [Robustness and Transferability of Pix2Geomodel for Bidirectional Facies Property Translation in a Complex Reservoir](https://mlsanity.com/paper/2605.03919/) (2026)

## Abstract (arXiv)

Deep learning techniques are increasingly being considered for geological applications where -- much like in computer vision -- the challenges are characterized by high-dimensional spatial data dominated by multipoint statistics. In particular, a novel technique called generative adversarial networks has been recently studied for geological parametrization and synthesis, obtaining very impressive results that are at least qualitatively competitive with previous methods. The method obtains a neural network parametrization of the geology -- so-called a generator -- that is capable of reproducing very complex geological patterns with dimensionality reduction of several orders of magnitude. Subsequent works have addressed the conditioning task, i.e. using the generator to generate realizations honoring spatial observations (hard data). The current approaches, however, do not provide a parametrization of the conditional generation process. In this work, we propose a method to obtain a parametrization for direct generation of conditional realizations. The main idea is to simply extend the existing generator network by stacking a second inference network that learns to perform the conditioning. This inference network is a neural network trained to sample a posterior distribution derived using a Bayesian formulation of the conditioning task. The resulting extended neural network thus provides the conditional parametrization. Our method is assessed on a benchmark image of binary channelized subsurface, obtaining very promising results for a wide variety of conditioning configurations.