Training-image based geostatistical inversion using a spatial generative adversarial neural network

Abstract

Probabilistic inversion within a multiple-point statistics framework is often computationally prohibitive for high-dimensional problems. To partly address this, we introduce and evaluate a new training-image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generative adversarial network (GAN) type. After training using a training image (TI), our proposed spatial GAN (SGAN) can quickly generate 2D and 3D unconditional realizations. A key characteristic of our SGAN is that it defines a (very) low-dimensional parameterization, thereby allowing for efficient probabilistic inversion using state-of-the-art Markov chain Monte Carlo (MCMC) methods. In addition, available direct conditioning data can be incorporated within the inversion. Several 2D and 3D categorical TIs are first used to analyze the performance of our SGAN for unconditional geostatistical simulation. Training our deep network can take several hours. After training, realizations containing a few millions of pixels/voxels can be produced in a matter of seconds. This makes it especially useful for simulating many thousands of realizations (e.g., for MCMC inversion) as the relative cost of the training per realization diminishes with the considered number of realizations. Synthetic inversion case studies involving 2D steady-state flow and 3D transient hydraulic tomography with and without direct conditioning data are used to illustrate the effectiveness of our proposed SGAN-based inversion. For the 2D case, the inversion rapidly explores the posterior model distribution. For the 3D case, the inversion recovers model realizations that fit the data close to the target level and visually resemble the true model well.

References in corpus (6)

• Reconstruction of three-dimensional porous media using generative adversarial neural networks
• Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network
• Geological realism in hydrogeological and geophysical inverse modeling: a review
• Distributed soil moisture from crosshole ground-penetrating radar travel times using stochastic inversion
• Summary statistics from training images as prior information in probabilistic inversion
• Image synthesis with graph cuts: a fast model proposal mechanism in probabilistic inversion

Cited by in corpus (33)

• A trans-disciplinary review of deep learning research for water resources scientists
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media
• Deep Learning of Subsurface Flow via Theory-guided Neural Network
• Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification
• Towards a Robust Parameterization for Conditioning Facies Models Using Deep Variational Autoencoders and Ensemble Smoother
• Deep-learning-based surrogate flow modeling and geological parameterization for data assimilation in 3D subsurface flow
• Simulator-free Solution of High-Dimensional Stochastic Elliptic Partial Differential Equations using Deep Neural Networks
• Integration of adversarial autoencoders with residual dense convolutional networks for estimation of non-Gaussian hydraulic conductivities
• Multiphase flow prediction with deep neural networks
• Parametric generation of conditional geological realizations using generative neural networks
• Accurate and Fast reconstruction of Porous Media from Extremely Limited Information Using Conditional Generative Adversarial Network
• Deep-Learning based Inverse Modeling Approaches: A Subsurface Flow Example
• Deep generative models in inversion: a review and development of a new approach based on a variational autoencoder
• 3D CNN-PCA: A Deep-Learning-Based Parameterization for Complex Geomodels
• Solving inverse problems using conditional invertible neural networks
• Gradient-based deterministic inversion of geophysical data with Generative Adversarial Networks: is it feasible?
• Using Deep Learning to Improve Ensemble Smoother: Applications to Subsurface Characterization
• Recent Developments Combining Ensemble Smoother and Deep Generative Networks for Facies History Matching
• Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties
• Latent diffusion models for parameterization and data assimilation of facies-based geomodels
• Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems
• Informed Proposal Monte Carlo
• Variational Prior Replacement in Bayesian Inference and Inversion
• Introducing Conceptual Geological Information into Bayesian Tomographic Imaging
• Adaptive sequential Monte Carlo for posterior inference and model selection among complex geological priors
• Generating unrepresented proportions of geological facies using Generative Adversarial Networks
• Pixel-wise Conditioned Generative Adversarial Networks for Image Synthesis and Completion
• Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion
• Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications
• Diffusion models for multivariate subsurface generation and efficient probabilistic inversion
• 3D latent diffusion models for parameterizing and history matching multiscenario facies systems
• Generation of non-stationary stochastic fields using Generative Adversarial Networks