Balancing Accuracy and Speed: A Multi-Fidelity Ensemble Kalman Filter with a Machine Learning Surrogate Model

TL;DR

This paper introduces a multi-fidelity ensemble Kalman filter that integrates machine learning surrogate models as low-fidelity components, enhancing accuracy and computational efficiency in complex physical simulations like weather and ocean models.

Contribution

It proposes a novel MF-EnKF framework using ML surrogates as low-fidelity models, improving accuracy and speed without replacing the full physical model.

Findings

Higher accuracy than full replacement with ML models.

Improved accuracy within the same computational budget.

ML surrogate offers larger speed-up compared to low-resolution models.

Abstract

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 such a machine learning surrogate model, instead of 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 the 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 to the low-resolution one, but it can provide a larger speed-up. Our method contributes to increasing the effective ensemble size in the EnKF, which improves the estimation of the initial condition and hence accuracy of the predictions in fields such as meteorology and oceanography.