# History Matching under Uncertainty of Geological Scenarios with Implicit Geological Realism Control with Generative Deep Learning and Graph Convolutions

arXiv: https://arxiv.org/abs/2507.10201 · HTML: https://mlsanity.com/paper/2507.10201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 15 of 15)

- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [On Characterizing the Capacity of Neural Networks using Algebraic Topology](https://mlsanity.com/paper/1802.04443/) (2018)
- [Training-image based geostatistical inversion using a spatial generative adversarial neural network](https://mlsanity.com/paper/1708.04975/) (2017)
- [Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network](https://mlsanity.com/paper/1710.09196/) (2017)
- [On the Latent Space of Wasserstein Auto-Encoders](https://mlsanity.com/paper/1802.03761/) (2018)
- [Parametric generation of conditional geological realizations using generative neural networks](https://mlsanity.com/paper/1807.05207/) (2018)
- [Towards a Robust Parameterization for Conditioning Facies Models Using Deep Variational Autoencoders and Ensemble Smoother](https://mlsanity.com/paper/1812.06900/) (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)
- [Recent Developments Combining Ensemble Smoother and Deep Generative Networks for Facies History Matching](https://mlsanity.com/paper/2005.10638/) (2020)
- [DeepFlow: History Matching in the Space of Deep Generative Models](https://mlsanity.com/paper/1905.05749/) (2019)
- [Exemplar-based synthesis of geology using kernel discrepancies and generative neural networks](https://mlsanity.com/paper/1809.07748/) (2018)

## Abstract (arXiv)

The graph-based variational autoencoder represents an architecture that can handle the uncertainty of different geological scenarios, such as depositional or structural, through the concept of a lowerdimensional latent space. The main difference from recent studies is utilisation of a graph-based approach in reservoir modelling instead of the more traditional lattice-based deep learning methods. We provide a solution to implicitly control the geological realism through the latent variables of a generative model and Geodesic metrics. Our experiments of AHM with synthetic dataset that consists of 3D realisations of channelised geological representations with two distinct scenarios with one and two channels shows the viability of the approach. We offer in-depth analysis of the latent space using tools such as PCA, t-SNE, and TDA to illustrate its structure.