Deep Learning for Latent Space Data Assimilation LSDA in Subsurface Flow Systems

We present a deep learning architecture for efficient reduced-order implementation of ensemble data assimilation. Specifically, deep learning is used to improve two important aspects of data assimilation workflows: (i) low-rank representation of complex reservoir property distributions for geologically consistent feature-based model updating, and (ii) efficient prediction of the statistical information that are required for model updating. The proposed method uses deep convolutional autoencoders to nonlinearly map the original complex and high-dimensional parameters onto a low-dimensional parameter latent space that compactly represents the original parameters. In addition, a low-dimensional data latent space is constructed to predict the observable response of each model parameter realization, which can be used to compute the statistical information needed for the data assimilation step. The two mappings are developed as a joint deep learning architecture with two autoencoders that are connected and trained together. The training uses an ensemble of model parameters and their corresponding production response predictions as needed in implementing the standard ensemble-based data assimilation frameworks. Simultaneous training of the two mappings leads to a joint data-parameter manifold that captures the most salient information in the two spaces for a more effective data assimilation, where only relevant data and parameter features are included. Moreover, the parameter-to-data mapping provides a fast forecast model that can be used to increase the ensemble size for a more accurate data assimilation, without a major computational overhead. We implement the developed approach to a series of numerical experiments, including a 3D example based on the Volve field in the North Sea. For data assimilation methods that involve iterative schemes, such as ensemble smoothers with multiple data assimilation or iterative forms of ensemble Kalman filter, the proposed approach offers a computationally competitive alternative. Our results show that a fully low-dimensional implementation of ensemble data assimilation using deep learning architectures offers several advantages compared to standard algorithms, including joint data-parameter reduction that respects the salient features in each space, geologically consistent feature-based updates, increased ensemble sizes to improve the accuracy and computational efficiency of the calculated statistics for the update step.