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A stable deep adversarial learning approach for geological facies generation

Ferdinand Bhavsar, Nicolas Desassis, Fabien Ors, Thomas Romary

TL;DR

Results indicate that by utilizing recent stabilization techniques, generative adversarial networks can efficiently sample from target data distributions and demonstrate the ability to simulate conditioned simulations through the latent variable model property of the proposed approach.

Abstract

The simulation of geological facies in an unobservable volume is essential in various geoscience applications. Given the complexity of the problem, deep generative learning is a promising approach to overcome the limitations of traditional geostatistical simulation models, in particular their lack of physical realism. This research aims to investigate the application of generative adversarial networks and deep variational inference for conditionally simulating meandering channels in underground volumes. In this paper, we review the generative deep learning approaches, in particular the adversarial ones and the stabilization techniques that aim to facilitate their training. The proposed approach is tested on 2D and 3D simulations generated by the stochastic process-based model Flumy. Morphological metrics are utilized to compare our proposed method with earlier iterations of generative adversarial networks. The results indicate that by utilizing recent stabilization techniques, generative adversarial networks can efficiently sample from target data distributions. Moreover, we demonstrate the ability to simulate conditioned simulations through the latent variable model property of the proposed approach.

A stable deep adversarial learning approach for geological facies generation

TL;DR

Results indicate that by utilizing recent stabilization techniques, generative adversarial networks can efficiently sample from target data distributions and demonstrate the ability to simulate conditioned simulations through the latent variable model property of the proposed approach.

Abstract

The simulation of geological facies in an unobservable volume is essential in various geoscience applications. Given the complexity of the problem, deep generative learning is a promising approach to overcome the limitations of traditional geostatistical simulation models, in particular their lack of physical realism. This research aims to investigate the application of generative adversarial networks and deep variational inference for conditionally simulating meandering channels in underground volumes. In this paper, we review the generative deep learning approaches, in particular the adversarial ones and the stabilization techniques that aim to facilitate their training. The proposed approach is tested on 2D and 3D simulations generated by the stochastic process-based model Flumy. Morphological metrics are utilized to compare our proposed method with earlier iterations of generative adversarial networks. The results indicate that by utilizing recent stabilization techniques, generative adversarial networks can efficiently sample from target data distributions. Moreover, we demonstrate the ability to simulate conditioned simulations through the latent variable model property of the proposed approach.
Paper Structure (25 sections, 3 theorems, 34 equations, 18 figures, 4 tables)

This paper contains 25 sections, 3 theorems, 34 equations, 18 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Stable stationnary GAN
  3. Conditioning the generator to observations
  4. Variational Bayes Conditioning
  5. Inference Network
  6. Mixture of Gaussians
  7. Application
  8. Flumy
  9. Experimental setup
  10. Meandering channelized reservoir simulations results
  11. 2D
  12. 3D
  13. Parameterized Model
  14. Conditional Generation
  15. 2D
  16. ...and 10 more sections

Key Result

Theorem B.1.1

Let $p_r$ and $p_\theta$ be two probability distributions defined on a probability space $M$. Let $\Pi$ be the set of all joint distributions such that $p_r$ and $p_\theta$ are the marginal distributions. Let $\gamma$ be an element of $\Pi$ and let $(x, y)$ be realizations of $\gamma$. The Wasserste

Figures (18)

  • Figure 1: Following the method from chan_shing_gan_channelized, we use a secondary network that will transform a random vector $\hat{z}$ into our conditional posterior $z|x^\star$.
  • Figure 2: Overview of Flumy's main simulated processes for Fluvial systems flumy
  • Figure 3: Comparison of the proportions of different facies for our 2D models.
  • Figure 4: Distribution of connected components size of each geological facies for different models against training data. To make visualisation more relevant, each connected component size is itself weighted by it's volume.
  • Figure 5: Comparison of the generated realisations (on the left) to their nearest counterparts in the training dataset (on the right) using Euclidean distance.
  • ...and 13 more figures

Theorems & Definitions (3)

  • Theorem B.1.1
  • Theorem B.2.1
  • Theorem B.3.1