Balancing accuracy and speed: A multi‐fidelity ensemble Kalman filter with a machine learning surrogate model

Currently, more and more machine learning (ML) surrogates are being developed for computationally expensive physical models. In this work we investigate the use of a multi‐fidelity ensemble Kalman filter (MF‐EnKF) in which the low‐fidelity model is an ML surrogate, rather than a traditional low‐resolution or reduced‐order model. The idea behind this is to use an ensemble of a few expensive full model runs, together with an ensemble of many cheap but less accurate ML model runs. In this way we hope to reach increased accuracy within the same computational budget. We investigate the performance by testing the approach on two common test problems; namely, the Lorenz‐2005 model and a quasi‐geostrophic model. By keeping the original physical model in place, we obtain a higher accuracy than when we completely replace it by the ML model. Furthermore, the MF‐EnKF reaches improved accuracy within the same computational budget. The ML surrogate has similar or improved accuracy compared with the low‐resolution one, but it can provide a larger speed‐up. Our method contributes to increasing the effective ensemble size in the ensemble Kalman filter, which improves the estimation of the initial condition and hence accuracy of the predictions in fields such as meteorology and oceanography.