315 research outputs found
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
Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network
Efficient and high-fidelity prior sampling and inversion for complex
geological media is still a largely unsolved challenge. Here, we use a deep
neural network of the variational autoencoder type to construct a parametric
low-dimensional base model parameterization of complex binary geological media.
For inversion purposes, it has the attractive feature that random draws from an
uncorrelated standard normal distribution yield model realizations with spatial
characteristics that are in agreement with the training set. In comparison with
the most commonly used parametric representations in probabilistic inversion,
we find that our dimensionality reduction (DR) approach outperforms principle
component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform
(DCT) DR techniques for unconditional geostatistical simulation of a
channelized prior model. For the considered examples, important compression
ratios (200 - 500) are achieved. Given that the construction of our
parameterization requires a training set of several tens of thousands of prior
model realizations, our DR approach is more suited for probabilistic (or
deterministic) inversion than for unconditional (or point-conditioned)
geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D
transient hydraulic tomography data are used to demonstrate the DR-based
inversion. For the 2D case study, the performance is superior compared to
current state-of-the-art multiple-point statistics inversion by sequential
geostatistical resampling (SGR). Inversion results for the 3D application are
also encouraging
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
Machine learning methods for uncertainty quantification in subsurface reservoirs
We investigate current challenges in the reservoir engineering pipeline that can be addressed using recent machine learning techniques. Our emphasis is on improving the performance of uncertainty quantification tasks which are ubiquitous in subsurface reservoir simulations. In one work, we accelerate multiscale methods by embedding a neural network surrogate for the fast computation of the custom basis functions, replacing the need to solve the local elliptic problems normally required to obtain them. In a different work, we address current challenges in obtaining geological parametrizations that can capture complex geological structures. We adopt a neural network parametrization using a recent unsupervised learning technique, obtaining an effective parametrization that can reproduce high-order statistics of flow responses. In a follow-up work, we introduce a method for post-hoc conditioning of the neural network parametrization to generate conditional realizations by training a second neural network to sample from a Bayesian posterior and coupling it with the original network. In our final work, we introduce a framework for exemplar-based parametric synthesis of geological images based on a recent kernel method, obtaining a neural network parametrization of the geology using a single exemplar image
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