4,213 research outputs found
History Matching Using Principal Component Analysis
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Improved integration of information to reduce subsurface model bias
Subsurface modeling deals with data-related issues like cognitive and sampling biases, and model-related challenges including statistical assumptions, misspecification, and algorithmic biases. These challenges introduce four critical implications during subsurface modeling. Firstly, subsurface sampling is subject to sampling bias, which compromises statistical representativeness. Secondly, analog selection methodologies rely on multivariate statistics and expert judgment that overlook spatial information and data dimensionality. Thirdly, subsurface inferential workflows that utilize dimensionality reduction seldom provide repeatable frameworks that maintain model stability and are invariant to Euclidean transformations. Lastly, deep learning methods for dimensionality reduction, characterized as black-box models, lack interpretability and robust evaluation metrics, increasing susceptibility to algorithmic bias. Consequently, neglecting these challenges in subsurface modeling could lead to erroneous predictions, inconsistent inferences, diminished model reliability, and suboptimal decision-making that impacts project economics.
This dissertation integrates information within subsurface models to reduce model bias and significantly improve their accuracy, robustness, and generalizability. First, I create spatial declustering methods to debias spatial datasets with single and multiscale preferential sampling in stationary populations. Second, I introduce a novel geostatistics-based machine learning method for identifying subsurface resource analogs that integrate spatial information in subsurface datasets with high dimensionality. Next, I efficiently combine machine learning and computational geometry methods to stabilize lower dimensional spaces for uncertainty quantification and interpretation. Finally, I create a methodology to assess, evaluate, and interpret the stability of deep learning latent feature spaces.
These novel methodologies demonstrate the importance of improved techniques for information integration in subsurface modeling and show better results over naïve methods. This results in objective sampling debiasing in spatial stationary populations with single or multiple data scales, improving statistical representativity. Also, the results show better generalization and accurate identification of spatial analogs in high-dimensional datasets. Moreover, the methods yield Euclidean transformation-invariant lower-dimensional spaces, ensuring unique and repeatable solutions that improve model reliability and interpretability, for rational comparisons. Finally, the results indicate that deep learning models for dimensionality reduction exhibit algorithmic biases and instabilities, including sample, structural, and inferential instability, affecting their reliability and interpretability. Together, these innovations ultimately reduce model bias and significantly improve subsurface modeling.Petroleum and Geosystems Engineerin
4D Seismic History Matching Incorporating Unsupervised Learning
The work discussed and presented in this paper focuses on the history
matching of reservoirs by integrating 4D seismic data into the inversion
process using machine learning techniques. A new integrated scheme for the
reconstruction of petrophysical properties with a modified Ensemble Smoother
with Multiple Data Assimilation (ES-MDA) in a synthetic reservoir is proposed.
The permeability field inside the reservoir is parametrised with an
unsupervised learning approach, namely K-means with Singular Value
Decomposition (K-SVD). This is combined with the Orthogonal Matching Pursuit
(OMP) technique which is very typical for sparsity promoting regularisation
schemes. Moreover, seismic attributes, in particular, acoustic impedance, are
parametrised with the Discrete Cosine Transform (DCT). This novel combination
of techniques from machine learning, sparsity regularisation, seismic imaging
and history matching aims to address the ill-posedness of the inversion of
historical production data efficiently using ES-MDA. In the numerical
experiments provided, I demonstrate that these sparse representations of the
petrophysical properties and the seismic attributes enables to obtain better
production data matches to the true production data and to quantify the
propagating waterfront better compared to more traditional methods that do not
use comparable parametrisation techniques
Generating Subsurface Earth Models using Discrete Representation Learning and Deep Autoregressive Network
Subsurface earth models (referred to as geo-models) are crucial for
characterizing complex subsurface systems. Multiple-point statistics are
commonly used to generate geo-models. In this paper, a deep-learning-based
generative method is developed as an alternative to the traditional Geomodel
generation procedure. The generative method comprises two deep-learning models,
namely the hierarchical vector-quantized variational autoencoder (VQ-VAE-2) and
PixelSNAIL autoregressive model. Based on the principle of neural discrete
representation learning, the VQ-VAE-2 learns to massively compress the
Geomodels to extract the low-dimensional, discrete latent representation
corresponding to each Geomodel. Following that, PixelSNAIL uses the deep
autoregressive network to learn the prior distribution of the latent codes. For
the purpose of Geomodel generation, PixelSNAIL samples from the newly learned
prior distribution of latent codes, and then the decoder of the VQ-VAE-2
converts the newly sampled latent code to a newly constructed geo-model.
PixelSNAIL can be used for unconditional or conditional geo-model generation.
In an unconditional generation, the generative workflow generates an ensemble
of geo-models without any constraint. On the other hand, in the conditional
geo-model generation, the generative workflow generates an ensemble of
geo-models similar to a user-defined source image, which ultimately facilitates
the control and manipulation of the generated geo-models. To better construct
the fluvial channels in the geo-models, the perceptual loss is implemented in
the VQ-VAE-2 model instead of the traditional mean squared error loss. At a
specific compression ratio, the quality of multi-attribute geo-model generation
is better than that of single-attribute geo-model generation
Making the most of data:An information selection and assessment framework to improve water systems operations
Advances in Environmental monitoring systems are making a wide range of data available at increasingly higher temporal and spatial resolution. This creates an opportunity to enhance real-time understanding of water systems conditions and to improve prediction of their future evolution, ultimately increasing our ability to make better decisions. Yet, many water systems are still operated using very simple information systems, typically based on simple statistical analysis and the operator’s experience. In this work, we propose a framework to automatically select the most valuable information to inform water systems operations supported by quantitative metrics to operationally and economically assess the value of this information. The Hoa Binh reservoir in Vietnam is used to demonstrate the proposed framework in a multiobjective context, accounting for hydropower production and flood control. First, we quantify the expected value of perfect information, meaning the potential space for improvement under the assumption of exact knowledge of the future system conditions. Second, we automatically select the most valuable information that could be actually used to improve the Hoa Binh operations. Finally, we assess the economic value of sample information on the basis of the resulting policy performance. Results show that our framework successfully select information to enhance the performance of the operating policies with respect to both the competing objectives, attaining a 40% improvement close to the target trade-off selected as potentially good compromise between hydropower production and flood control
Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems
One of the major challenges in the Bayesian solution of inverse problems
governed by partial differential equations (PDEs) is the computational cost of
repeatedly evaluating numerical PDE models, as required by Markov chain Monte
Carlo (MCMC) methods for posterior sampling. This paper proposes a data-driven
projection-based model reduction technique to reduce this computational cost.
The proposed technique has two distinctive features. First, the model reduction
strategy is tailored to inverse problems: the snapshots used to construct the
reduced-order model are computed adaptively from the posterior distribution.
Posterior exploration and model reduction are thus pursued simultaneously.
Second, to avoid repeated evaluations of the full-scale numerical model as in a
standard MCMC method, we couple the full-scale model and the reduced-order
model together in the MCMC algorithm. This maintains accurate inference while
reducing its overall computational cost. In numerical experiments considering
steady-state flow in a porous medium, the data-driven reduced-order model
achieves better accuracy than a reduced-order model constructed using the
classical approach. It also improves posterior sampling efficiency by several
orders of magnitude compared to a standard MCMC method
An efficient polynomial chaos-based proxy model for history matching and uncertainty quantification of complex geological structures
A novel polynomial chaos proxy-based history matching and uncertainty quantification
method is presented that can be employed for complex geological structures in inverse
problems. For complex geological structures, when there are many unknown geological
parameters with highly nonlinear correlations, typically more than 106 full reservoir
simulation runs might be required to accurately probe the posterior probability space
given the production history of reservoir. This is not practical for high-resolution geological
models. One solution is to use a "proxy model" that replicates the simulation
model for selected input parameters. The main advantage of the polynomial chaos
proxy compared to other proxy models and response surfaces is that it is generally
applicable and converges systematically as the order of the expansion increases. The
Cameron and Martin theorem 2.24 states that the convergence rate of the standard
polynomial chaos expansions is exponential for Gaussian random variables. To improve
the convergence rate for non-Gaussian random variables, the generalized polynomial
chaos is implemented that uses an Askey-scheme to choose the optimal basis for polynomial
chaos expansions [199]. Additionally, for the non-Gaussian distributions that
can be effectively approximated by a mixture of Gaussian distributions, we use the
mixture-modeling based clustering approach where under each cluster the polynomial
chaos proxy converges exponentially fast and the overall posterior distribution can be
estimated more efficiently using different polynomial chaos proxies.
The main disadvantage of the polynomial chaos proxy is that for high-dimensional problems,
the number of the polynomial chaos terms increases drastically as the order of the
polynomial chaos expansions increases. Although different non-intrusive methods have
been developed in the literature to address this issue, still a large number of simulation
runs is required to compute high-order terms of the polynomial chaos expansions. This
work resolves this issue by proposing the reduced-terms polynomial chaos expansion
which preserves only the relevant terms in the polynomial chaos representation. We
demonstrated that the sparsity pattern in the polynomial chaos expansion, when used
with the Karhunen-Loéve decomposition method or kernel PCA, can be systematically
captured.
A probabilistic framework based on the polynomial chaos proxy is also suggested in the
context of the Bayesian model selection to study the plausibility of different geological
interpretations of the sedimentary environments. The proposed surrogate-accelerated
Bayesian inverse analysis can be coherently used in practical reservoir optimization
workflows and uncertainty assessments
Probabilistic load forecasting with Reservoir Computing
Some applications of deep learning require not only to provide accurate
results but also to quantify the amount of confidence in their prediction. The
management of an electric power grid is one of these cases: to avoid risky
scenarios, decision-makers need both precise and reliable forecasts of, for
example, power loads. For this reason, point forecasts are not enough hence it
is necessary to adopt methods that provide an uncertainty quantification.
This work focuses on reservoir computing as the core time series forecasting
method, due to its computational efficiency and effectiveness in predicting
time series. While the RC literature mostly focused on point forecasting, this
work explores the compatibility of some popular uncertainty quantification
methods with the reservoir setting. Both Bayesian and deterministic approaches
to uncertainty assessment are evaluated and compared in terms of their
prediction accuracy, computational resource efficiency and reliability of the
estimated uncertainty, based on a set of carefully chosen performance metrics
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