Model‐Reduced Adjoint‐Based Inversion Using Deep‐Learning: Example of Geological Carbon Sequestration Modeling

As an extension of our previous research on deep‐learning‐based adjoint‐state approach (Xiao, Deng, & Wang, 2021, https://doi.org/10.1029/2020wr027400), we present a two‐level hybrid neural network architecture to efficiently derive a model‐reduced adjoint‐based optimization workflow with a large‐scale inverse modeling example in geological carbon‐storage applications. The first level employs a nonlinear dimensionality reduction technique, that is, deep convolutional autoencoder, owing to its high scalability and the availability of high‐performance deep‐learning libraries for flexible implementation. Analogous to the reduced‐order linear model, the second level emulates a neural‐network‐powered linear transition unit based on the reduced subspace. This hybrid framework provides a readily available model‐reduced adjoint derivation with negligible computational cost and computer storage. Once the gradient is obtained in reduced space, it is correspondingly projected back to full space for the inverse modeling. The performance of the method is verified by estimating the space‐dependent stochastic permeability field using two geological carbon storage (GCS) process‐based multiphase flow models with an increasing complexity. The experimental results indicate that the surrogate model can accurately characterize the spatial‐temporal evolution of the CO₂ saturation fields using a relatively small number of training data. Although the proposed inversion workflow achieves comparable results similar to the conventional finite‐difference method, it is faster than high‐fidelity model simulations in several orders of magnitude; hence, it will be a beneficial simulation and modeling tool for engineers to manage the uncertainty of GCS processing.