Surrogate-assisted inversion for large-scale history matching: Comparative study between projection-based reduced-order modeling and deep neural network

History matching can play a key role in improving geological characterization and reducing the uncertainty of reservoir model predictions. Application of reservoir history matching is restricted by the huge computational cost by amongst others the many runs of the full model. Surrogate models with a reduced complexity are therefore used to reduce the computational demands. This paper presents an efficient surrogate-assisted deterministic inversion framework to primarily explore the possibility of applying deep neural network (DNN) surrogate to approximate the gradient of large-scale history matching by using auto-differentiation (AD). In combination with the deep neural network model, the AD enables us to evaluate the gradients efficiently in a parallel manner. Furthermore, the benefits of using stochastic gradient optimizers in the deep learning practice, instead of full gradient optimizers in conventional deterministic inversions, is investigated as well. Numerical experiments are conducted on a 3D benchmark reservoir model in the context of a water-flooding production scenario. The quantity of interest, e.g., dynamic saturation for an ensemble of test models, can be accurately predicted. The proposed surrogate-assisted inversion with stochastic gradient optimizer obtains a very quick convergence rate against the model and data noise for the high-dimensional history matching problem with a large number of data and parameters. In addition, we also conduct several comparisons and evaluations with our previously proposed projection-based subdomain POD-TPWL approach in terms of computational efficiency and accuracy. The subdomain POD-TPWL constructs a local surrogate model, which is repeatedly reconstructed a number of times for maintaining a satisfactory accuracy, while DNN constructs a global surrogate model based on the entire training data and generally does not require additional reconstructions. The subdomain POD-TPWL is very sensitive to how the domain is decomposed, increasing the training samples does not infinitely improve the history matching results by a fixed decomposition. Overall, these two kinds of surrogate models have demonstrated great potential in solving large-scale history matching problem. The DNN surrogate is particularly useful to generate multiple posteriors for model uncertainty quantification.