An adaptive Gaussian process-based iterative ensemble smoother for data assimilation

Accurate characterization of subsurface hydraulic conductivity is vital for modeling of subsurface flow and transport. The iterative ensemble smoother (IES) has been proposed to estimate the heterogeneous parameter field. As a Monte Carlo-based method, IES requires a relatively large ensemble size to guarantee its performance. To improve the computational efficiency, we propose an adaptive Gaussian process (GP)-based iterative ensemble smoother (GPIES) in this study. At each iteration, the GP surrogate is adaptively refined by adding a few new base points chosen from the updated parameter realizations. Then the sensitivity information between model parameters and measurements is calculated from a large number of realizations generated by the GP surrogate with virtually no computational cost. Since the original model evaluations are only required for base points, whose number is much smaller than the ensemble size, the computational cost is significantly reduced. The applicability of GPIES in estimating heterogeneous conductivity is evaluated by the saturated and unsaturated flow problems, respectively. Without sacrificing estimation accuracy, GPIES achieves about an order of magnitude of speed-up compared with the standard IES. Although subsurface flow problems are considered in this study, the proposed method can be equally applied to other hydrological models.