Efficient Data Assimilation with Latent-Space Representations for Subsurface Flow Systems

Abstract:

We present an efficient deep learning-based approach for data assimilation in subsurface flow systems with Latent-Space representations. To perform data assimilation, we perform dimensionality reduction to identify a joint data-parameter manifold, in which a mapping from model latent space to data latent space is established. The low-dimensional manifold is learned by using the prior distribution of model parameters and the related simulated responses as training data in a deep learning architecture consisting of a pair of convolutional autoencoders. The latent space variables compactly represent the spatial geologic features of model realizations and the corresponding temporal features of the simulated flow response data. The parameter-to-data mapping in the latent space is used to develop a compact proxy model to speed up the forecast step of data assimilation methods. Additionally, the latent-space representation offers an effective parameterization of high-dimensional model parameters with complex spatial distributions, which can result in updated models that are geologically more consistent with the prior continuity model. We demonstrate the effectiveness of latent space representations for implementing data assimilation in subsurface flow systems using a variant of the Ensemble Kalman Filter known as the Ensemble Smoother with multiple data assimilation (ES-MDA). The latent-space representation is simultaneously trained to perform dimensionality reduction and nonlinear forward mapping from model to data space, which are combined to perform data assimilation efficiently. We demonstrate the performance of this approach using large-scale 3D examples, including complex fluvial models with non-Gaussian spatial patterns. The compact representations of the data and models in the latent space alleviates the computational burden associated with running forward simulations and allows for a reduced representation of geologic features to preserve the expected geological continuity in the updated models.