# Recent Developments Combining Ensemble Smoother and Deep Generative Networks for Facies History Matching

arXiv: https://arxiv.org/abs/2005.10638 · HTML: https://mlsanity.com/paper/2005.10638/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2020.

## Built on by (most cited first, 8 of 8)

- [Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19](https://mlsanity.com/paper/2105.07729/) (2021)
- [Latent diffusion models for parameterization and data assimilation of facies-based geomodels](https://mlsanity.com/paper/2406.14815/) (2024)
- [Generative Network-Based Reduced-Order Model for Prediction, Data Assimilation and Uncertainty Quantification](https://mlsanity.com/paper/2105.13859/) (2021)
- [3D latent diffusion models for parameterizing and history matching multiscenario facies systems](https://mlsanity.com/paper/2508.16621/) (2025)
- [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)
- [Enhancing the Parameterization of Reservoir Properties for Data Assimilation Using Deep VAE-GAN](https://mlsanity.com/paper/2603.18766/) (2026)
- [Data assimilation for subsurface flow using latent diffusion model parameterization: performance of ensemble-Kalman and Monte Carlo techniques](https://mlsanity.com/paper/2606.11140/) (2026)
- [Parameterization method of reservoir properties for ensemble-based data assimilation using intermediate latent space of StyleGAN](https://mlsanity.com/paper/2609.39626/) (2026)

## Abstract (arXiv)

Ensemble smoothers are among the most successful and efficient techniques currently available for history matching. However, because these methods rely on Gaussian assumptions, their performance is severely degraded when the prior geology is described in terms of complex facies distributions. Inspired by the impressive results obtained by deep generative networks in areas such as image and video generation, we started an investigation focused on the use of autoencoders networks to construct a continuous parameterization for facies models. In our previous publication, we combined a convolutional variational autoencoder (VAE) with the ensemble smoother with multiple data assimilation (ES-MDA) for history matching production data in models generated with multiple-point geostatistics. Despite the good results reported in our previous publication, a major limitation of the designed parameterization is the fact that it does not allow applying distance-based localization during the ensemble smoother update, which limits its application in large-scale problems. The present work is a continuation of this research project focusing in two aspects: firstly, we benchmark seven different formulations, including VAE, generative adversarial network (GAN), Wasserstein GAN, variational auto-encoding GAN, principal component analysis (PCA) with cycle GAN, PCA with transfer style network and VAE with style loss. These formulations are tested in a synthetic history matching problem with channelized facies. Secondly, we propose two strategies to allow the use of distance-based localization with the deep learning parameterizations.