Adaptive Multifidelity Data Assimilation for Nonlinear Subsurface Flow Problems

Abstract Ensemble‐based methods have been widely used for characterization of model parameters. Due to their Monte Carlo nature, these methods can be easily implemented but usually need relatively large ensemble sizes to guarantee the accuracy, resulting in a high computational cost. To address this issue, we propose an adaptive multifidelity ensemble smoother for data assimilation, which takes advantage of both the accuracy of a high‐fidelity (HF) model and the efficiency of a low‐fidelity (LF) model. In this work, an ensemble smoother‐based multiple data assimilation scheme is employed. In the forecast step, a large number of LF simulations and a small number of HF simulations are implemented. By exploring the correlations between the predictions of HF and LF models, a multifidelity Gaussian process is established to serve as a surrogate for the original system without sacrificing accuracy. To consider the surrogate errors and avoid the underestimation of uncertainties in the analysis step, the ensemble smoother‐based multiple data assimilation scheme is amended with extra iterations. After each analysis step, the multifidelity Gaussian process surrogate is locally refined in the posterior region. In summary, the expensive HF model evaluations are implemented only if necessary. The efficiency of the proposed method is illustrated by a synthetic case and a real‐world experiment. It is shown that even though the majority of model evaluations are implemented using the LF models in an adaptive multifidelity ensemble smoother, the accuracy is not sacrificed. The proposed multifidelity framework is with the general applicability since it can be equally combined with other ensemble‐based data assimilation methods.