Generating Infinite-Resolution Texture using GANs with Patch-by-Patch Paradigm

In this paper, we introduce a novel approach for generating texture images of infinite resolutions using Generative Adversarial Networks (GANs) based on a patch-by-patch paradigm. Existing texture synthesis techniques often rely on generating a large-scale texture using a one-forward pass to the generating model, this limits the scalability and flexibility of the generated images. In contrast, the proposed approach trains GANs models on a single texture image to generate relatively small patches that are locally correlated and can be seamlessly concatenated to form a larger image while using a constant GPU memory footprint. Our method learns the local texture structure and is able to generate arbitrary-size textures, while also maintaining coherence and diversity. The proposed method relies on local padding in the generator to ensure consistency between patches and utilizes spatial stochastic modulation to allow for local variations and diversity within the large-scale image. Experimental results demonstrate superior scalability compared to existing approaches while maintaining visual coherence of generated textures.

Gym-preCICE: Reinforcement Learning Environments for Active Flow Control

Active flow control (AFC) involves manipulating fluid flow over time to achieve a desired performance or efficiency. AFC, as a sequential optimisation task, can benefit from utilising Reinforcement Learning (RL) for dynamic optimisation. In this work, we introduce Gym-preCICE, a Python adapter fully compliant with Gymnasium (formerly known as OpenAI Gym) API to facilitate designing and developing RL environments for single- and multi-physics AFC applications. In an actor-environment setting, Gym-preCICE takes advantage of preCICE, an open-source coupling library for partitioned multi-physics simulations, to handle information exchange between a controller (actor) and an AFC simulation environment. The developed framework results in a seamless non-invasive integration of realistic physics-based simulation toolboxes with RL algorithms. Gym-preCICE provides a framework for designing RL environments to model AFC tasks, as well as a playground for applying RL algorithms in various AFC-related engineering applications.

Probabilistic forecasting for geosteering in fluvial successions using a generative adversarial network

Quantitative workflows utilizing real-time data to constrain ahead-of-bit uncertainty have the potential to improve geosteering significantly. Fast updates based on real-time data are essential when drilling in complex reservoirs with high uncertainties in pre-drill models. However, practical assimilation of real-time data requires effective geological modeling and mathematically robust parameterization. We propose a generative adversarial deep neural network (GAN), trained to reproduce geologically consistent 2D sections of fluvial successions. Offline training produces a fast GAN-based approximation of complex geology parameterized as a 60-dimensional model vector with standard Gaussian distribution of each component. Probabilistic forecasts are generated using an ensemble of equiprobable model vector realizations. A forward-modeling sequence, including a GAN, converts the initial (prior) ensemble of realizations into EM log predictions. An ensemble smoother minimizes statistical misfits between predictions and real-time data, yielding an update of model vectors and reduced uncertainty around the well. Updates can be then translated to probabilistic predictions of facies and resistivities. The present paper demonstrates a workflow for geosteering in an outcrop-based, synthetic fluvial succession. In our example, the method reduces uncertainty and correctly predicts most major geological features up to 500 meters ahead of drill-bit.

Generation of non-stationary stochastic fields using Generative Adversarial Networks with limited training data

In the context of generating geological facies conditioned on observed data, samples corresponding to all possible conditions are not generally available in the training set and hence the generation of these realizations depends primary on the generalization capability of the trained generative model. The problem becomes more complex when applied on non-stationary fields. In this work, we investigate the problem of training Generative Adversarial Networks (GANs) models against a dataset of geological channelized patterns that has a few non-stationary spatial modes and examine the training and self-conditioning settings that improve the generalization capability at new spatial modes that were never seen in the given training set. The developed training method allowed for effective learning of the correlation between the spatial conditions (i.e. non-stationary maps) and the realizations implicitly without using additional loss terms or solving a costly optimization problem at the realization generation phase. Our models, trained on real and artificial datasets were able to generate geologically-plausible realizations beyond the training samples with a strong correlation with the target maps.

Generating unrepresented proportions of geological facies using Generative Adversarial Networks

In this work, we investigate the capacity of Generative Adversarial Networks (GANs) in interpolating and extrapolating facies proportions in a geological dataset. The new generated realizations with unrepresented (aka. missing) proportions are assumed to belong to the same original data distribution. Specifically, we design a conditional GANs model that can drive the generated facies toward new proportions not found in the training set. The presented study includes an investigation of various training settings and model architectures. In addition, we devised new conditioning routines for an improved generation of the missing samples. The presented numerical experiments on images of binary and multiple facies showed good geological consistency as well as strong correlation with the target conditions.

Optimal Bayesian experimental design for subsurface flow problems

Optimal Bayesian design techniques provide an estimate for the best parameters of an experiment in order to maximize the value of measurements prior to the actual collection of data. In other words, these techniques explore the space of possible observations and determine an experimental setup that produces maximum information about the system parameters on average. Generally, optimal Bayesian design formulations result in multiple high-dimensional integrals that are difficult to evaluate without incurring significant computational costs as each integration point corresponds to solving a coupled system of partial differential equations. In the present work, we propose a novel approach for development of polynomial chaos expansion (PCE) surrogate model for the design utility function. In particular, we demonstrate how the orthogonality of PCE basis polynomials can be utilized in order to replace the expensive integration over the space of possible observations by direct construction of PCE approximation for the expected information gain. This novel technique enables the derivation of a reasonable quality response surface for the targeted objective function with a computational budget comparable to several single-point evaluations. Therefore, the proposed technique reduces dramatically the overall cost of optimal Bayesian experimental design. We evaluate this alternative formulation utilizing PCE on few numerical test cases with various levels of complexity to illustrate the computational advantages of the proposed approach.

Parametrization of stochastic inputs using generative adversarial networks with application in geology

We investigate artificial neural networks as a parametrization tool for stochastic inputs in numerical simulations. We address parametrization from the point of view of emulating the data generating process, instead of explicitly constructing a parametric form to preserve predefined statistics of the data. This is done by training a neural network to generate samples from the data distribution using a recent deep learning technique called generative adversarial networks. By emulating the data generating process, the relevant statistics of the data are replicated. The method is assessed in subsurface flow problems, where effective parametrization of underground properties such as permeability is important due to the high dimensionality and presence of high spatial correlations. We experiment with realizations of binary channelized subsurface permeability and perform uncertainty quantification and parameter estimation. Results show that the parametrization using generative adversarial networks is very effective in preserving visual realism as well as high order statistics of the flow responses, while achieving a dimensionality reduction of two orders of magnitude.

Exemplar-based synthesis of geology using kernel discrepancies and generative neural networks

We propose a framework for synthesis of geological images based on an exemplar image. We synthesize new realizations such that the discrepancy in the patch distribution between the realizations and the exemplar image is minimized. Such discrepancy is quantified using a kernel method for two-sample test called maximum mean discrepancy. To enable fast synthesis, we train a generative neural network in an offline phase to sample realizations efficiently during deployment, while also providing a parametrization of the synthesis process. We assess the framework on a classical binary image representing channelized subsurface reservoirs, finding that the method reproduces the visual patterns and spatial statistics (image histogram and two-point probability functions) of the exemplar image.

Parametric generation of conditional geological realizations using generative neural networks

We introduce a method for parametric generation of conditional geological realizations using generative neural networks. We build on our recent work where we trained a neural network to generate unconditional geological realizations using generative adversarial networks. Here we propose a method for post-hoc conditioning of pre-trained generator networks to generate conditional realizations. We frame the problem in the Bayesian setting and model the posterior distribution of the latent vector given observations. To efficiently generate multiple latent vector solutions, we train a neural network to generate samples from the posterior distribution. This inference network is trained by minimizing the discrepancy between its output distribution and the posterior. Once the inference network is trained, it is coupled to the (unconditional) generator to obtain the conditional generator, thus also maintaining a parametrization of the (conditional) generation process.

A machine learning approach for efficient uncertainty quantification using multiscale methods

Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these coarse scale basis functions. Specifically, we employ a neural network predictor fitted using a set of solution samples from which it learns to generate subsequent basis functions at a lower computational cost than solving the local problems. The computational advantage of this approach is realized for uncertainty quantification tasks where a large number of realizations has to be evaluated. We attribute the ability to learn these basis functions to the modularity of the local problems and the redundancy of the permeability patches between samples. The proposed method is evaluated on elliptic problems yielding very promising results.