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.
In CS231N class, we have learned two different approaches to image generation in the context of deep learning: Variational Auto-Encoder (VAE) @cite_16 and Generative Adversarial Networks (GAN) @cite_8 . In @cite_0 , a conditional U-Net for shape-guided image generation, conditioned on the output of a VAE for appearance is presented. The separation between shape and appearance is carefully modelled and thus an explicit representation of the appearance, which can be combined with new poses, is obtained. Motivated by this work, we established the analogue between shape-guided image and control-guided saturation map. Similarly, the hidden appearance in image is analogous to the underlying permeability map. Under this framework, the variational U-Net is trained to learn the underlying Darcy's law. We take advantages of the nature of CNN, allowing the freedom of saturation map generation under various well controls. Efficient uncertainty quantification tasks can be conducted then to provide valuable evaluations of potential injection plans.
@cite_0 @cite_16 @cite_8
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Deep generative models have demonstrated great performance in image synthesis. However, results deteriorate in case of spatial deformations, since they generate images of objects directly, rather than modeling the intricate interplay of their inherent shape and appearance. We present a conditional U-Net for shape-guided image generation, conditioned on the output of a variational autoencoder for appearance. The approach is trained end-to-end on images, without requiring samples of the same object with varying pose or appearance. Experiments show that the model enables conditional image generation and transfer. Therefore, either shape or appearance can be retained from a query image, while freely altering the other. Moreover, appearance can be sampled due to its stochastic latent representation, while preserving shape. In quantitative and qualitative experiments on COCO, DeepFashion, shoes, Market-1501 and handbags, the approach demonstrates significant improvements over the state-of-the-art. "If I provide you a face image of mine (without telling you the actual age when I took the picture) and a large amount of face images that I crawled (containing labeled faces of different ages but not necessarily paired), can you show me what I would look like when I am 80 or what I was like when I was 5?" The answer is probably a "No." Most existing face aging works attempt to learn the transformation between age groups and thus would require the paired samples as well as the labeled query image. In this paper, we look at the problem from a generative modeling perspective such that no paired samples is required. In addition, given an unlabeled image, the generative model can directly produce the image with desired age attribute. We propose a conditional adversarial autoencoder (CAAE) that learns a face manifold, traversing on which smooth age progression and regression can be realized simultaneously. In CAAE, the face is first mapped to a latent vector through a convolutional encoder, and then the vector is projected to the face manifold conditional on age through a deconvolutional generator. The latent vector preserves personalized face features (i.e., personality) and the age condition controls progression vs. regression. Two adversarial networks are imposed on the encoder and generator, respectively, forcing to generate more photo-realistic faces. Experimental results demonstrate the appealing performance and flexibility of the proposed framework by comparing with the state-of-the-art and ground truth. If I provide you a face image of mine (without telling you the actual age when I took the picture) and a large amount of face images that I crawled (containing labeled faces of different ages but not necessarily paired), can you show me what I would look like when I am 80 or what I was like when I was 5? The answer is probably a No. Most existing face aging works attempt to learn the transformation between age groups and thus would require the paired samples as well as the labeled query image. In this paper, we look at the problem from a generative modeling perspective such that no paired samples is required. In addition, given an unlabeled image, the generative model can directly produce the image with desired age attribute. We propose a conditional adversarial autoencoder (CAAE) that learns a face manifold, traversing on which smooth age progression and regression can be realized simultaneously. In CAAE, the face is first mapped to a latent vector through a convolutional encoder, and then the vector is projected to the face manifold conditional on age through a deconvolutional generator. The latent vector preserves personalized face features (i.e., personality) and the age condition controls progression vs. regression. Two adversarial networks are imposed on the encoder and generator, respectively, forcing to generate more photo-realistic faces. Experimental results demonstrate the appealing performance and flexibility of the proposed framework by comparing with the state-of-the-art and ground truth. The task of face attribute manipulation has found increasing applications, but still remains challeng- ing with the requirement of editing the attributes of a face image while preserving its unique details. In this paper, we choose to combine the Variational AutoEncoder (VAE) and Generative Adversarial Network (GAN) for photorealistic image genera- tion. We propose an effective method to modify a modest amount of pixels in the feature maps of an encoder, changing the attribute strength contin- uously without hindering global information. Our training objectives of VAE and GAN are reinforced by the supervision of face recognition loss and cy- cle consistency loss for faithful preservation of face details. Moreover, we generate facial masks to en- force background consistency, which allows our training to focus on manipulating the foreground face rather than background. Experimental results demonstrate our method, called Mask-Adversarial AutoEncoder (M-AAE), can generate high-quality images with changing attributes and outperforms prior methods in detail preservation.