Quantification of uncertainty in production injection forecasting is an important aspect of reservoir simulation studies. Conventional approaches include intrusive Galerkin-based methods (e.g., generalized polynomial chaos (gPC) and stochastic collocation (SC) methods) and non-intrusive Monte Carlo (MC) based methods. Nevertheless, the quantification is conducted in reformulations of the underlying stochastic PDEs with fixed well controls. If one wants to take various well control plans into account, expensive computations need to be repeated for each well design independently. In this project, we take advantages of the equation-free spirit of convolutional neural network (CNN) to overcome this challenge and thus achieve the flexibility of efficient uncertainty quantification with various well controls. We are interested in the development of surrogate models for uncertainty quantification and propagation in reservoir simulations using a deep convolutional encoder-decoder network as an analogue to the image-to-image regression tasks in computer science. First, a U-Net architecture is applied to replace conventional expensive deterministic PDE solver. Then we adopt the idea from shape-guided image generation using variational U-Net and design a new variational U-Net architecture for "control-guided" reservoir simulation. Backward propagation is learned in the network to extract the hidden physical quantities and then predict the future production by the learned forward propagation using the hidden variable with various well controls. Comparisons in computational efficiency are made between our proposed CNN approach and conventional MC approach. Significant improvements in computational speed with reasonable accuracy loss are observed in the numerical tests.
Recently, deep learning has been explored as a competitive methodology across fields such as fluid mechanics @cite_25 , hydrology @cite_24 @cite_3 , bioinformatics @cite_15 , high energy physics @cite_11 and others. In particular, @cite_10 adopted an end-to-end image-to image regression approach for surrogate modeling governed by stochastic PDEs with high-dimensional stochastic input in random porous media. In addition, the deep neural networks are set under a formal Bayesian formula to enable the network to express its uncertainty on its predictions when using limited training data. @cite_10 and our project both study two-dimensional, single phase, steady-state flow through a random permeability field. However, the emphasis of @cite_10 lies in Bayesian deep learning dealing with high dimensional random inputs but with fixed single well control. In this work, we focus on uncertainty propagation with , which would allow existing well information to infer the incomplete uncertain geological properties and evaluate potential well locations during simulation. In large-scale reservoir project like CCS, such quantification from simulations will be of significant importance and economic value in industry.
@cite_3 @cite_24 @cite_15 @cite_10 @cite_25 @cite_11
2767537294 2311607323 2784733489 2585298970 2125621954
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. In the era of big data, transformation of biomedical big data into valuable knowledge has been one of the most important challenges in bioinformatics. Deep learning has advanced rapidly since the early 2000s and now demonstrates state-of-the-art performance in various fields. Accordingly, application of deep learning in bioinformatics to gain insight from data has been emphasized in both academia and industry. Here, we review deep learning in bioinformatics, presenting examples of current research. To provide a useful and comprehensive perspective, we categorize research both by the bioinformatics domain (i.e. omics, biomedical imaging, biomedical signal processing) and deep learning architecture (i.e. deep neural networks, convolutional neural networks, recurrent neural networks, emergent architectures) and present brief descriptions of each study. Additionally, we discuss theoretical and practical issues of deep learning in bioinformatics and suggest future research directions. We believe that this review will provide valuable insights and serve as a starting point for researchers to apply deep learning approaches in their bioinformatics studies. Abstract We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder–decoder network in a similar fashion to approaches considered in deep learning for image-to-image regression tasks. Since normal neural networks are data-intensive and cannot provide predictive uncertainty, we propose a Bayesian approach to convolutional neural nets. A recently introduced variational gradient descent algorithm based on Stein's method is scaled to deep convolutional networks to perform approximate Bayesian inference on millions of uncertain network parameters. This approach achieves state of the art performance in terms of predictive accuracy and uncertainty quantification in comparison to other approaches in Bayesian neural networks as well as techniques that include Gaussian processes and ensemble methods even when the training data size is relatively small. To evaluate the performance of this approach, we consider standard uncertainty quantification tasks for flow in heterogeneous media using limited training data consisting of permeability realizations and the corresponding velocity and pressure fields. The performance of the surrogate model developed is very good even though there is no underlying structure shared between the input (permeability) and output (flow pressure) fields as is often the case in the image-to-image regression models used in computer vision problems. Studies are performed with an underlying stochastic input dimensionality up to 4225 where most other uncertainty quantification methods fail. Uncertainty propagation tasks are considered and the predictive output Bayesian statistics are compared to those obtained with Monte Carlo estimates. It was only a matter of time before deep neural networks (DNNs) – deep learning – made their mark in turbulence modelling, or more broadly, in the general area of high-dimensional, complex dynamical systems. In the last decade, DNNs have become a dominant data mining tool for big data applications. Although neural networks have been applied previously to complex fluid flows, the article featured here ( , J. Fluid Mech. , vol. 807, 2016, pp. 155–166) is the first to apply a true DNN architecture, specifically to Reynolds averaged Navier Stokes turbulence models. As one often expects with modern DNNs, performance gains are achieved over competing state-of-the-art methods, suggesting that DNNs may play a critically enabling role in the future of modelling complex flows. High-energy particle colliders are important for finding new particles, but huge volumes of data must be searched through to locate them. Here, the authors show the use of deep-learning methods on benchmark data sets as an approach to improving such new particle searches.