An adaptive Kriging surrogate method for efficient uncertainty quantification with an application to geological carbon sequestration modeling

In numerical modeling of geological carbon sequestration (GCS), uncertainty quantification (UQ) is usually needed to evaluate the impact of uncertain model parameters on model predictions caused by limited measurements and incomplete knowledge of the parameters. However, UQ for GCS is computationally expensive due to the large ensemble of complex and lengthy model simulations. In this study, we propose an adaptive Kriging method to build a fast-to-evaluate surrogate of the GCS model to alleviate the heavy computational burden. The surrogate model is efficiently generated using a Taylor expansion-based adaptive experimental design algorithm that combines a distance-based exploration criterion and an exploitation criterion to adaptively search for informative training samples. In addition, we analyze the uncertainty brought by substituting the surrogate for the actual simulation model and explore its influence on UQ results. Our method is demonstrated in a synthetic GCS model and its performance is evaluated in comparison with the conventional Monte Carlo sampling. Results indicate that our method can greatly improve the computational efficiency in UQ and provide an effective and reliable UQ solution with the consideration of surrogate uncertainty.