Abstract
Parametrization is widely used to improve the solution of ill-posed subsurface flow model calibration problems. Traditional low-dimensional parameterization methods consist of spatial and transform-domain methods with well-established mathematical properties that are mostly amenable to interpretation. More recent deep learning-based parametrization approaches exhibit strong performance in representing complex geological patterns but lack interpretability, making them less suitable for systematic updates based on expert knowledge. We present a disentangled parameterization approach with variational autoencoder (VAE) architecture to enable improved representation of complex spatial patterns and provide some degree of interpretability by allowing certain spatial features and attributes of a property map to be controlled by a single latent variable (generative factor), while remaining relatively invariant to changes in other latent factors. The existence of disentangled latent variables brings extra controllability to incorporate expert knowledge in making updates to the model. We explore two different approaches to achieve disentangled parameterization. In the first approach, we use β-VAE to learn disentangled factors in unsupervised learning manner, while in the second approach we apply the conditional VAE to represent discrete disentangled factors through supervised learning. By encoding the geologic scenarios into discrete latent codes, the parameterization enables automated scenario selection during inverse modeling and assisted updates on the spatial maps by experts. We present preliminary results using a single-phase pumping test example to show how model calibration can benefit from the proposed disentangled parameterization.
